Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1)
When solving a system of equations using matrices, we first rewrite the system as an augmented
matrix. Which of the following is included in the augmented matrix?
1)
A)
Only constant terms of the system
B)
Only coefficients of the system
C)
Coefficients and constant terms of the system
D)
None of the above
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
2)
Write a problem for a classmate to solve by translating to a system of two equations in two
variables. Devise the problem so that the solution is “The Cobras made 5 three–point
baskets and 28 two–point baskets.”
2)
3)
A student argued that it is impossible to use the substitution method to determine if a
system of equations has no solution or an infinite number of solutions. Is the student
correct?
3)
4)
Write a problem for a classmate to solve by translating to a system of two equations in two
variables.
4)
5)
In solving a system of three equations in three variables, the final step yields the following
equation: 0 = 1. How many solutions does this system have? Explain geometrically.
5)
6)
Explain why the solution of a system of equations is the point of intersection of the graphs
of the equations.
6)
7)
A student solved the system of equations
x + 2y = 4
4x + 8y =16
for x in the first equation, and substituted into the second equation. The y’s also
disappeared in the process. The student claimed that the system of equations has no
solution. Is this correct?
7)
8)
Describe two advantages of the substitution method over the graphing method for solving
systems of equations.
8)
9)
Describe the three possible outcomes when graphing a system of equations, and relate each
to the type of solution(s) each system has.
9)
10)
In solving a system of three equations in three variables, the final step yields the following
equation: 0 = 0. How many solutions does this system have? Explain geometrically.
10)
1
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the system using substitution.
11)
y = 2x – 1
4y – 16x = -36
A)
(7, 4)
B)
(4, 7)
C)
all ordered pairs that solve y =2x – 1
D)
no solution
Provide an appropriate response.
12)
Write an expression that illustrates the quantity described.
The monetary value (in dollars) of x dimes and y quarters.
A)
$10x + $25y
B)
$.35(x + y)
C)
$.10x + $.25y
D)
$.25x + $.10y
Solve using a matrix on a graphing calculator.
13)
2x – y – 5z = -24
-6x + 2y – 4z = -30
-3x – 7y + z = -56
A)
(-4, 7, 8)
B)
(4, 7, 5)
C)
(4, 5, 7)
D)
No solution
14)
-4x – y – 4z = -27
8x + 2y – 7z = –21
-6x – 5y + z = -16
A)
(1, 5, 3)
B)
(1, 3, 5)
C)
(-1, 3, 2)
D)
No solution
Translate to a system of two equations, then solve.
15)
From a point on a river, two boats are driven in opposite directions, one at 8 miles per hour and the
other at 9 miles per hour. In how many hours will they be 85 miles apart?
A)
5 hours
B)
7 hours
C)
1 hour
D)
6 hours
Provide an appropriate response.
16)
What is the graph of an equation in three variables?
A)
A triangle
B)
A plane
C)
A pyramid
D)
A line
Determine whether the system of equations is consistent with independent equations, consistent with dependent
equations, or inconsistent.
17)
3x + 2y = -1
6x + 4y = -2
A)
Consistent with independent equations
B)
Consistent with dependent equations
C)
Inconsistent
2
Solve the system of equations.
18)
x + y + z = 2
x – y + 3z = -6
3x + y + z = 10
A)
(-3, 4, 1)
B)
(-3, 1, 4)
C)
(4, 1, -3)
D)
No solution
Translate to a system of two equations, then solve.
19)
The perimeter of a rectangle is 86 m. If the width were doubled and the length were increased by 8
m, the perimeter would be 140 m. What are the length and width of the rectangle?
A)
Width 16 m, length 21 m
B)
Width 19 m, length 24 m
C)
Width 21 m, length 21 m
D)
Width 24 m, length 19 m
Graph the solution of the system.
20)
4x < 3y
(4x + 3y) -10
A)
B)
3
C)
D)
Translate the problem to a system of equations, then solve using matrices.
21)
Jim wants to plan a meal with 74 grams of carbohydrates and 620 calories. If green beans have 7
grams of carbohydrates and 30 calories per half cup serving and if french fried shrimp have 9
grams of carbohydrates and 190 calories per three–ounce serving, how many servings of green
beans and shrimp should he use?
A)
7 half cups of beans and 9 three–ounce helpings of shrimp
B)
8 half cups of beans and 2 three–ounce helpings of shrimp
C)
2 half cups of beans and 8 three–ounce helpings of shrimp
D)
9 half cups of beans and 7 three–ounce helpings of shrimp
Solve the problem.
22)
After retirement, Kelly’s company offers her two options for receiving her retirement pension.
According the the first plan, she will receive monthly payments from a variable annuity that
initially pays $700 per month then decreases each month at a rate of $25 per month per year.
Optionally, she may choose a plan that pays her a fixed amount of $500 per month for the rest of
her life. The monthly payments for the two plans are illustrated in the graph below. After how
many years does the variable plan pay less per month than the fixed plan?
A)
9 years
B)
Up to 8 years
C)
8 years
D)
The variable plan always pays less.
4
Solve the system of equations.
23)
2x + 4y + 8z = 48
x + 2y + 4z = -12
x + y + z = -4
A)
(-2, 2, -4)
B)
(-4, -2, 2)
C)
(-4, 2, -2)
D)
No solution
Provide an appropriate response.
24)
Write an expression that illustrates the quantity described.
The actual speed of a boat that goes 18.3 miles per hour against a current of 2.5 miles per hour.
A)
20.8 miles per hour
B)
15.8 miles per hour
C)
2.5 miles per hour
D)
18.3 miles per hour
Write the augmented matrix for the system of equations.
25)
5x + 7y = –3
7y = 7
A)
5 7 –3
0 7 7
B)
–3 7 5
70 7
C)
7 0 7
5 7 7
D)
5 7 –3
770
Determine whether the system of equations is consistent with independent equations, consistent with dependent
equations, or inconsistent.
26)
y = x – 9
y + 4 = x
A)
Consistent with dependent equations
B)
Inconsistent
C)
Consistent with independent equations
Solve the system using substitution.
27)
4x – 2y = 108
x = -4y
A)
all ordered pairs that solve 4x – 2y =108
B)
no solution
C)
(24, -6)
D)
(-6, 24)
Solve the system of equations.
28)
7x – y + 9z = 48
–4x + 6z = 12
8y + z = 76
A)
(-3, 9, 6)
B)
(3, 9, 4)
C)
(3, 4, 9)
D)
No solution
Provide an appropriate response.
29)
Write an expression that illustrates the quantity described.
The cost of m student tickets and n adult tickets for a play if a student ticket costs $9.00 and an
adult ticket costs $7.00
A)
$9.00m + $7.00n
B)
$16.00(m + n)
C)
$16.00
D)
$(m + n)
5
30)
Decide if the system has one solution, no solution, or an infinite number of solutions.
4x – 16y =12
y =1
4x –3
4
A)
None
B)
One
C)
Infinite number
Solve the system using elimination.
31)
3x + 4y = 1
6x + 3y = 1
A)
1
15, – 1
5
B)
– 1
5, – 1
15
C)
1
15, 1
5
D)
1
5, 1
15
Solve the system of equations.
32)
x – y + 3z = 11
x + 5y + z = –23
0.4x + 0.1z = 0.2
A)
(0, –5, 2)
B)
(2, –5, 0)
C)
(2, 0, –5)
D)
No solution
Solve the system using elimination.
33)
4x + y =–18
3x + 4y = –7
A)
no solution
B)
(2, –5)
C)
(–5, 2)
D)
(0, 2)
Provide an appropriate response.
34)
Write an expression that illustrates the quantity described.
The cost of z pounds of candy that sell for $3.24 per pound.
A)
$z
B)
$3.25z
C)
$3.24
D)
$3.24z
Translate the problem to a system of equations, then solve using matrices.
35)
A croissant, a cup of coffee, and a fruit bowl from Kelley’s Coffee Cart cost a total of $5.50, and a
croissant costs twice as much as a cup of coffee. Kelley posts a notice announcing that, effective
next week, the price of a croissant will go up 15% and the price of coffee will go up 15%. After the
increase, the total price of the purchase will be $5.84. Find the cost of each item before the increase.
A)
A fruit bowl costs $3.25, a croissant costs $1.50, and a cup of coffee costs $0.75.
B)
A fruit bowl costs $3.25, a croissant costs $0.86, and a cup of coffee costs $1.73.
C)
A fruit bowl costs $3.25, a croissant costs $1.73, and a cup of coffee costs $0.86.
D)
The prices cannot be determined from the given information.
Translate to a system of three equations, then solve.
36)
Michael’s bank contains only nickels, dimes, and quarters. There are 49 coins in all, valued at $3.85.
The number of nickels is 3 short of being three times the sum of the number of dimes and quarters
together. How many dimes are in the bank?
A)
36
B)
13
C)
5
D)
8
6
Translate into a system of equations. Do not solve.
37)
Anne has 25 coins in her pocket consisting of nickels and dimes only. The total value of the coins is
$1.95. How many nickels and how many dimes does she have? (Let x represent the number of
nickels and y represent the number of dimes.)
A)
x + y = 25
5x + 10y = 195
B)
x + y = 25
0.05x + 0.1y = 195
C)
x + y = 25
5x + 5y = 195
D)
x + y = 25
5x + 10y = 1.95
Solve the system using elimination.
38)
x– 6y = -42
–6x – 7y = -6
A)
no solution
B)
(-7, 7)
C)
(6, 7)
D)
(-6, 6)
39)
1
5x – 1
4 y = 3
2
5x + 1
2y = 3
A)
no solution
B)
45
4, -3
C)
all ordered pairs that solve 1
5x –1
4 y =3
D)
– 45
4, -6
Solve the problem.
40)
Bruce is a retired carpenter who builds patio chairs and dog houses, which he sells at his local flea
market. It takes him 5 hours to build a dog house and 3 hours to build a patio chair. Bruce can work
no more than 25 hours per week, and he must produce more chairs than dog houses. Write a
system of inequalities to describe this situation. Use D for the number of dog houses and P for the
number of patio chairs produced in a week.
A)
P + D > 0
P + D 25
B)
P D
3P + 5D < 25
C)
3P > 5D
P + D 25
D)
P > D
3P + 5D 25
Solve by transforming the augmented matrix into row echelon form.
41)
2x + 5y = 15
2x + 2y = 0
A)
(-5, -5)
B)
no solution
C)
(-5, 5)
D)
(5, -5)
Indicate whether the statement is true or false.
42)
It is impossible for a system of two linear inequalities to have exactly one solution.
A)
True
B)
False
7
Determine whether the given ordered pair is a solution to the given system of equations.
43)
(4, –4); 4x – y = 20
3x – 4y = 28
A)
Yes
B)
No
Solve using a matrix on a graphing calculator.
44)
9x – 7y = 45
5x – 2y = 25
A)
(5, 1)
B)
(4, 1)
C)
(5, 0)
D)
No solution
Solve the system of equations.
45)
x – y + 4z = 2
2x + z = 0
x + 5y + z = –10
A)
(0, 0, –2)
B)
(0, –2, 2)
C)
(0, –2, 0)
D)
No solution
Translate to a system of two equations, then solve.
46)
During 2002 and 2003, a total of 5544 people were infected with a specific virus. In 2003, 3.53 times
as many people were infected as in 2002. How many people were infected each year? Round your
answer to the nearest whole number.
A)
4320 in 2002, 1224 in 2003
B)
1224 in 2002, 4320 in 2003
C)
3353 in 2002, 2191 in 2003
D)
2191 in 2002, 3353 in 2003
Translate into a system of equations. Do not solve.
47)
An isosceles triangle has a perimeter of 31 inches. The shortest side is 5 inches shorter than either of
the other two sides. Find the length of each side of the triangle (recall that an isosceles triangle has
two sides with equal measure.)
A)
x + 2y = 31
x – y = 5
B)
x + y = 31
x + y = 5
C)
2x + 2y = 31
x – y = 5
D)
2x + y = 31
x – y = 5
Solve by transforming the augmented matrix into row echelon form.
48)
-6x + 5y = 10
-2x – 3y = –6
A)
(0, 3)
B)
no solution
C)
(0, 2)
D)
(-1, 3)
Solve the system using substitution.
49)
x = –16 – 9y
2x + 8y = –22
A)
no solution
B)
(7, 0)
C)
(-7, –1)
D)
(-8, 0)
Translate to a system of three equations, then solve.
50)
The sum of three consecutive odd integers is 261. Find the integers.
A)
85, 87, 89
B)
89, 91, 93
C)
80, 81, 82
D)
87, 89, 91
8
Translate to a system of two equations, then solve.
51)
Two angles are complementary. The second angle measures 76° less than the first angle. What is the
measure of the first angle?
A)
173°
B)
17°
C)
83°
D)
104°
Translate into a system of equations. Do not solve.
52)
A truck is driven for 6 hours, part of the time at 30 miles per hour and the rest of the time at 60
miles per hour. The total distance traveled was 270 miles. How long did the truck travel at each
speed?
A)
x + y = 270
30x + 60y = 6
B)
x – y = 6
30x – 60y = 270
C)
x + y = 6
30x + 60y = 270
D)
x + y = 60
60x + 30y = 270
Complete the indicated row operation.
53)
Replace R2 in –48 5
-6 5 0 with R1+R2.
A)
-10 13 5
-10 13 5
B)
–4 4 5
-6 -1 0
C)
-10 13 5
-6 5 0
D)
–48 5
-10 13 5
Determine whether the ordered triple is a solution of the system.
54)
(–2, –1, 5)
x – y + z = 4
2x – 8y – 3z = 24
3x + 4y + 2z = 7
A)
Yes
B)
No
Translate the problem to a system of equations, then solve using matrices.
55)
John has a jarful of quarters and nickels. There are 104 coins in the jar. The value of the coins is
$14.60. How many of each type of coin?
A)
52 quarters and 52 nickels
B)
57 quarters and 47 nickels
C)
99 quarters and 5 nickels
D)
47 quarters and 57 nickels
Complete the indicated row operation.
56)
Replace R2 in –1-9 -1
2 3 0 with 1
2R2.
A)
–1
2– 9
2– 1
2
13
2 0
B)
–1-9 1
13
2 0
C)
–1
2– 9
2– 1
2
2 3 0
D)
–1-9 1
4 6 0
9
Solve using a matrix on a graphing calculator.
57)
1.2x – 2.2y – 5.0z = 3.4
3.2x – 1.9y + 0.6z = -3.8
2.6x – 4.6y – 2.5z = 8.6
A)
(–18.2, -20.2, 1.1)
B)
(–3.6, -4.0, 0.2)
C)
(–7.3, -8.1, 0.5)
D)
(–14.5, -16.2, 0.9)
Translate to a system of three equations, then solve.
58)
A object is thrown upward with an initial velocity of v0 from an initial height of h. The height of
the object, h, is described by an equation of the form h = at2+v0t +h0, where h and h0 are in feet
and t is in seconds. The table below shows the height for different values of t. Find the values of a,
v0, and h0 and write the equation for h.
t h
1334
9654
10 550
A)
a = –16, v0=200, h0=150; h = –16t2+200t +150
B)
a = –16, v0=150, h0=200; h = –16t2+150t +200
C)
a = 16, v0=150, h0=200; h = –16t2+150t +200
D)
a = 16, v0=200, h0=150; h = 16t2+200t +150
Write the augmented matrix for the system of equations.
59)
2x + 7z = 13
3y + 2z = 17
8x + 4y + 2z = 46
A)
2 0 8 13
0 3 417
7 2 2 46
B)
2 0 7 13
0 3 2 17
84246
C)
2 7 0 13
3 2 0 17
84246
D)
2 0 7
0 3 2
842
Solve the system using substitution.
60)
y = 5
6x
5x – 6y = 0
A)
– 3
5, 1
2
B)
no solution
C)
– 3
5, –1
2
D)
3
5, –1
2
Indicate whether the statement is true or false.
61)
If one inequality in a system of two linear inequalities contains the “<” symbol and the other
contains the “>” symbol, the graph of the system will have solid boundary lines.
A)
True
B)
False
10
Provide an appropriate response.
62)
Write an expression that illustrates the quantity described.
The amount of pure antifreeze in a solution of x quarts of 27% antifreeze.
A)
27x quarts
B)
.27x quarts
C)
x quarts
D)
.27 quarts
Determine whether the ordered triple is a solution of the system.
63)
(-5, -4, 4)
x + 3y + 5z = -13
5y + 5z = 0
z = -4
A)
Yes
B)
No
Translate to a system of two equations, then solve.
64)
Justin and Tisha are hiking north along the same trail. Tisha is hiking at a comfortable rate of 2 mph
and passes a large hollow hickory tree at 4:36 PM. Justin is speeding along at a brisk rate of 4 mph
and passes the tree at 5:06 PM. At what time will Justin catch up to Tisha?
A)
5:46 PM
B)
5:51 PM
C)
5:31 PM
D)
5:36 PM
Solve the system graphically.
65)
y = -20 – 3x
x + 6y = -18
A)
(-6, -2)
B)
(-8, 4)
C)
(-6, -7)
D)
(6, -2)
Describe the next row operation that should be performed to make the matrix closer to row echelon form.
66)
1 9 7-4
011 –7-3
0–1-5 12
A)
Replace R2 with R1+R2.
B)
Replace R2 with – 1
11 R2.
C)
Replace R2 with 1
11R2.
D)
Replace R1 with 1
9R1.
11
Explain the mistake in the graph.
67)
x + y < –3
x – y 1
A)
x – y 1 should be a dotted line.
B)
x – y 1 is shaded on the wrong side.
C)
x + y < –3 is shaded on the wrong side.
D)
x + y < –3 should be a solid line.
Determine whether the ordered triple is a solution of the system.
68)
(–3, –1, 4)
2x – 2y – 3z = -16
4x – 3y + 3z = 3
x + y – 5z = -24
A)
Yes
B)
No
Provide an appropriate response.
69)
What is echelon form?
A)
The coefficient portion of the augmented matrix has 1’s on the diagonal from lower right to
upper left and 0’s below the 1’s.
B)
The coefficient portion of the augmented matrix has 1’s on the diagonal from upper left to
lower right and 0’s above the 1′s.
C)
The coefficient portion of the augmented matrix has 1’s on the diagonal from upper right to
lower left and 0’s below the 1’s.
D)
The coefficient portion of the augmented matrix has 1’s on the diagonal from upper left to
lower right and 0‘s below the 1’s.
Solve by transforming the augmented matrix into row echelon form.
70)
–3x – y + 4z = 5
4x – 3z = -1
2y + z = 23
A)
no solution
B)
(5, 7, 8)
C)
(5, 8, 7)
D)
(-5, 8, 10)
12
Solve using a matrix on a graphing calculator.
71)
2.5x + 2.2y – 1.5z = 2.5
5.3x – 5.4y + 1.0z = -2.3
3.3x + 3.8y + 4.2z = 10.5
A)
(2.3, 4.7, 4.0)
B)
(0.6, 1.2, 1.0)
C)
(1.1, 2.3, 2.0)
D)
(0.3, 0.6, 0.5)
Solve the system of equations.
72)
x – y + 3z = 1
-5x + 5y – 15z = 2
x + 5y + z = -23
A)
(0, -5, 2)
B)
(2, -5, 0)
C)
(2, 0, -5)
D)
No solution
Translate into a system of equations. Do not solve.
73)
The sum of two numbers is 34. The difference of the same numbers is 10. What are the numbers?
A)
x = 34
y = 10
B)
x + y = 34
x – y = 10
C)
x – y = 34
x + y = 10
D)
x + 34y = 0
10x + y = 0
Write the augmented matrix for the system of equations.
74)
6x + 5y + 8z = 34
8x + 5y – 2z = 48
4x – 2y + 9z = –13
A)
64 4 34
5 5 –248
8–2 9 –13
B)
6 5 8
8 5 –2
4–2 9
C)
6 5 8 34
8 5 –248
4–2 9 –13
D)
34 8 5 6
48 –2 5 8
–13 9–24
Complete the indicated row operation.
75)
Replace R3 in –6-5 -8 1
-4 9-10 0
52-1 -1 with 4R2+R3.
A)
–6-5 -8 1
-11 38 -41 -1
52-1 -1
B)
–6-5 -28 1
-4 926 0
52 7 -1
C)
–6-5 -8 1
16 17 -14 -4
52-1 -1
D)
–6-5 -8 1
-4 9-10 0
-11 38 -41 -1
Translate the problem to a system of equations, then solve using matrices.
76)
Anne and Nancy use a metal alloy that is 27.6% copper to make jewelry. How many ounces of a
24% alloy must be mixed with a 30% alloy to form 125 ounces of the desired alloy?
A)
52 ounces
B)
80 ounces
C)
50 ounces
D)
75 ounces
Write the augmented matrix for the system of equations.
77)
4x – 2y = 16
x + 6y = 24
A)
4–216
624 1
B)
6124
4–2–2
C)
4–216
0624
D)
4–216
1624
13
Indicate whether the statement is true or false.
78)
A system of two linear inequalities can have solutions in only one quadrant.
A)
True
B)
False
Graph the solution of the system.
79)
2x + y 4
x – 1 0
A)
B)
C)
D)
14
Complete the indicated row operation.
80)
Replace R1 in -8 –3 5 1
–510 1 1
8-11 20 with 1
6R1.
A)
-8 –3 5 1
–510 1 1
4
3– 11
6
1
30
B)
-8 –3 5 1
–5
65
3
1
6
1
6
8-11 20
C)
-48 –18 30 6
–510 1 1
8-11 20
D)
– 4
3–1
25
61
6
–510 1 1
8-11 20
Determine whether the given ordered pair is a solution to the given system of equations.
81)
(-5, 6); 2x + y = -16
4x + 2y = -32
A)
Yes
B)
No
Solve the system using substitution.
82)
6x + 9y = 57
-4x – 2y = –26
A)
(4, 4)
B)
(5, 4)
C)
no solution
D)
(5, 3)
Determine whether the ordered triple is a solution of the system.
83)
(0, 3, 2)
x – y + 3z = 3
4x + z = 2
x + 4y + z = 14
A)
Yes
B)
No
Solve by transforming the augmented matrix into row echelon form.
84)
x + 6y = 6
2x – 7y = -7
A)
(0, 1)
B)
(1, 0)
C)
(0, 0)
D)
(1, 1)
Solve the system of equations.
85)
2x + 4y + z = –27
3x – 3y – z = -2
5x + y + 2z = –31
A)
(-5, –4, –1)
B)
(–1, –4, -5)
C)
(-5, –1, –4)
D)
No solution
15
Solve the system graphically.
86)
3x + 2y = 29
3x – 2y = 13
A)
(3, 4)
B)
(7, 4)
C)
no solution
D)
(4, 7)
Determine whether the system of equations is consistent with independent equations, consistent with dependent
equations, or inconsistent.
87)
-6x + 5y = –12
42x – 35y = 84
A)
Consistent with dependent equations
B)
Inconsistent
C)
Consistent with independent equations
Determine whether the ordered triple is a solution of the system.
88)
(5, –4, 5)
2x – 3y + 3z = 24
4x + 4y – 3z = -8
3x – 3y + 2z = 23
A)
Yes
B)
No
Indicate whether the statement is true or false.
89)
A system of two linear inequalities can have solutions in exactly three of the quadrants.
A)
True
B)
False
16
Solve the problem.
90)
After retirement, Kelly’s company offers her two options for receiving her retirement pension.
According the the first plan, she will receive monthly payments from a variable annuity that
initially pays $700 per month then decreases each month at a rate of $25 per month per year.
Optionally, she may choose a plan that pays her a fixed amount of $500 per month for the rest of
her life. The monthly payments for the two plans are illustrated in the graph below. If Kelly’s
remaining life expectancy is 20 years, which plan would be the better choice?
A)
The fixed annuity
B)
The variable annuity
C)
Both plans are equally attractive.
Graph the solution of the system.
91)
x > -1
y 2
17
A)
B)
C)
D)
Solve the system using elimination.
92)
-5x – 4y = 2
15x + 12y = 6
A)
no solution
B)
(10, 8)
C)
all ordered pairs that solve -5x – 4y =2
D)
(-10, -8)
Translate to a system of two equations, then solve.
93)
A laser beam is aimed at a flat photocell at an angle. The angle on one side of the beam is 40° more
than the angle on the other side of the beam. Find the two angles.
A)
110°, 150°
B)
40°, 140°
C)
25°, 65°
D)
70°, 110°
Provide an appropriate response.
94)
Decide if the system has one solution, no solution, or an infinite number of solutions.
x + y =5
x + y =2
A)
Infinite number
B)
None
C)
One
18
Solve the system graphically.
95)
x = y – 6
5x = 3y
A)
(9, 15)
B)
(-9, 3)
C)
(0, 0)
D)
(15, 9)
Solve the system using elimination.
96)
-2x – 4y = 3
10x + 20y = -15
A)
(–6, -12)
B)
all ordered pairs that solve -2x – 4y =3
C)
(-12, –6)
D)
no solution
Translate the problem to a system of equations, then solve using matrices.
97)
A merchant has coffee worth $30 a pound that she wishes to mix with 50 pounds of coffee worth $
90 a pound to get a mixture that can be sold for $40 a pound. How many pounds of the $30 coffee
should be used?
A)
300 lb
B)
250 lb
C)
125 lb
D)
150 lb
Solve the system graphically.
98)
3x + y = 8
x + 5y = 26
A)
(1, 5)
B)
(4, -4)
C)
(1, 0)
D)
(-1, 5)
19
Determine whether the ordered triple is a solution of the system.
99)
(7, 2, –5)
3x – 8y + z = 0
2x + 4y – 3z = 37
-x + 2y – z = 2
A)
Yes
B)
No
Determine whether the system of equations is consistent with independent equations, consistent with dependent
equations, or inconsistent. How many solutions does the system have?
100)
100)
A)
Consistent with independent equations; one solution
B)
Inconsistent; no solution
C)
Consistent with dependent equations; infinite number of solutions
Given the matrix in row echelon form, find the solution for the system.
101)
12-5 4
0 1 -2 7
0 0 1 1
101)
A)
(1, 9, -9)
B)
(-9, 9, 1)
C)
(-1, 5, 1)
D)
(4, 7, 1)
Solve the system using elimination.
102)
0.6x + 0.6y = 4.8
0.8x – 0.4y = 0.4
102)
A)
(2.4, 11)
B)
(3, 11)
C)
(3, 5)
D)
(2.4, 5.6)
Write the augmented matrix for the system of equations.
103)
x + 5y = 69
5x – 2y + 5z = 0
8y – z = 44
103)
A)
1 5 1 69
5–2 5 0
18-1 44
B)
1 5 0 69
5–2 5 0
08-1 44
C)
1 5 0 69
5–2 5 0
08144
D)
1 5 0 69
5–2 5 0
8-1 044
20
Solve by transforming the augmented matrix into row echelon form.
104)
x – y + 3z = -11
2x + z = -2
x + 3y + z = 13
104)
A)
no solution
B)
(-2, 5, 0)
C)
(0, 5, -2)
D)
(-2, 0, 5)
Solve the system using substitution.
105)
-x + 8y = –7
3x– 24y = 4
105)
A)
no solution
B)
all ordered pairs that solve –x + 8y = –7
C)
(7, 0)
D)
0, –7
8
Provide an appropriate response.
106)
Write an expression that illustrates the quantity described.
The monetary value (in dollars) of n nickels.
106)
A)
$.05n
B)
$.10n
C)
$n
D)
$5n
107)
How many rows are in a 4×5 matrix?
107)
A)
5
B)
4
C)
9
D)
1
Translate into a system of equations. Do not solve.
108)
The sum of two numbers is -50. Five times the smaller number minus twice the larger number is
–47. What are the numbers? (Let x represent the smaller number and y represent the larger
number.)
108)
A)
x + y = -50
2x – 5y = –47
B)
x + y = -50
5x + 2y = –47
C)
x – y = -50
5x + 2y = –47
D)
x + y = -50
5x – 2y = –47
Determine whether the given ordered pair is a solution to the given system of equations.
109)
(-2, 5); x + y = 7
x – y = –3
109)
A)
Yes
B)
No
Graph the solution of the system.
21
110)
3x + y -1
y – x 1
x < 2
110)
A)
B)
C)
D)
Solve the system of equations.
111)
3x – y = 3
2y + z = 20
x + 4z = 35
111)
A)
(3, 6, 8)
B)
(6, 12, 16)
C)
(–3, –6, –8)
D)
No solution
22
Solve the system graphically.
112)
3x + y = 12
9x + 3y = 36
112)
A)
no solution
B)
all ordered pairs that solve 3x + y =12
C)
(5, -3)
D)
(0, 12)
Solve by transforming the augmented matrix into row echelon form.
113)
-5x – 9y – z = -88
x + 2y – 6z = -25
7x + y + z = 74
113)
A)
(-9, 4, 18)
B)
no solution
C)
(9, 7, 4)
D)
(9, 4, 7)
Indicate whether the statement is true or false.
114)
When graphing a system of two linear inequalities, the final shaded region is made up of all points
which belong to the graphs of either of the individual inequalities.
114)
A)
True
B)
False
Solve the system using elimination.
115)
x + y = 11
x – y = 5
115)
A)
(7, 4)
B)
(8, 3)
C)
(–8, 4)
D)
no solution
Translate to a system of three equations, then solve.
116)
A company sells nuts in bulk quantities. When bought in bulk, peanuts sell for $1.20 per pound,
almonds for $2.65 per pound, and cashews for $3.50 per pound. Suppose a specialty shop wants a
mixture of 400 pounds that will cost $2.93 per pound. Find the number of pounds of each type of
nut if the sum of the number of pounds of almonds and cashews is four times the number of
pounds of peanuts. Round your answers to the nearest pound.
116)
A)
Peanuts: 50 lb., almonds: 270 lb., cashews: 80 lb.
B)
Peanuts: 270 lb., almonds: 80 lb., cashews: 50 lb.
C)
Peanuts: 90 lb., almonds: 50 lb., cashews: 260 lb.
D)
Peanuts: 80 lb., almonds: 50 lb., cashews: 270 lb.
23
117)
In triangle ABC, the measure of angle B is 28° more than twice the measure of angle A. The
measure of angle C is 104° more than that of angle A. Find the angle measures.
117)
A)
8°, 44°, 128°
B)
12°, 52°, 104°
C)
15°, 58°, 107°
D)
12°, 52°, 116°
Given the matrix in row echelon form, find the solution for the system.
118)
1 3 –9
0 1 -1
118)
A)
(-12, -1)
B)
(-1, –6)
C)
(–9, -1)
D)
(–6, -1)
Translate to a system of three equations, then solve.
119)
A basketball fieldhouse seats 15,000. Courtside seats sell for $8, endzone for $7, and balcony for $4.
The total revenue from a sell–out is $78,000. If half the courtside and balcony seats and all the
endzone seats are sold, the total revenue is $46,000. How many of each type are there?
119)
A)
3200 courtside, 1800 endzone, 10,000 balcony
B)
3000 courtside, 3000 endzone, 8,000 balcony
C)
3000 courtside, 2000 endzone, 10,000 balcony
D)
4000 courtside, 3000 endzone, 8000 balcony
Write the augmented matrix for the system of equations.
120)
9x + 9y = 63
6x – 2y = 18
120)
A)
9 9 18
–2 6 63
B)
63 9 9
18 6–2
C)
9 6 63
9–218
D)
9 9 63
6–218
Determine whether the given ordered pair is a solution to the given system of equations.
121)
11
2, – 11
2; x – y = 0
x + y = 11
121)
A)
Yes
B)
No
Determine whether the system of equations is consistent with independent equations, consistent with dependent
equations, or inconsistent.
122)
-2x – y = -29
-8x – 4y = -118
122)
A)
Consistent with dependent equations
B)
Consistent with independent equations
C)
Inconsistent
Solve by transforming the augmented matrix into row echelon form.
123)
x + y = -7
x – y = 15
123)
A)
(4, 11)
B)
(7, -11)
C)
(4, -11)
D)
(7, 4)
Provide an appropriate response.
124)
If the y term is missing in both of two linear equations, the lines are ?
124)
A)
Coinciding
B)
Parallel
C)
Intersecting
D)
Parallel or Coinciding
24
Determine whether the ordered triple is a solution of the system.
125)
(–2, 6, –1)
-x + 3y + 4z = 16
3x + 2y – z = 7
4x – y + 3z = -17
125)
A)
Yes
B)
No
Translate to a system of three equations, then solve.
126)
The perimeter of a triangle is 37 inches. Twice the length of the longest side minus the length of the
shortest side is 28 inches. The sum of the length of the longest side and three times the sum of both
the other side lengths is 75 inches. Find the side lengths.
126)
A)
7in., 11 in., 19 in.
B)
8in., 12 in., 17 in.
C)
8in., 11 in., 18 in.
D)
No solution
Determine whether the given ordered pair is a solution to the given system of equations.
127)
(10, -4); 3
5x+ 4
5y = 14
5
6x + 2y =52
127)
A)
Yes
B)
No
Translate to a system of three equations, then solve.
128)
The sum of three consecutive integers is 447. Find the integers.
128)
A)
147, 148, 149
B)
147, 149, 151
C)
148, 149, 150
D)
149, 150, 151
Indicate whether the statement is true or false.
129)
A system of two linear inequalities can have solutions in all quadrants.
129)
A)
True
B)
False
Solve using a matrix on a graphing calculator.
130)
7x + 5y = 41
-4x – 2y = -20
130)
A)
(2, 5)
B)
(3, 4)
C)
(3, 5)
D)
No solution
25
Graph the solution of the system.
131)
x + 2y 2
x – y 0
131)
A)
B)
C)
D)
26
Determine whether the system of equations is consistent with independent equations, consistent with dependent
equations, or inconsistent. How many solutions does the system have?
132)
132)
A)
Inconsistent; no solution
B)
Consistent with independent equations; one solution
C)
Consistent with dependent equations; infinite number of solutions
Provide an appropriate response.
133)
How many columns are in a 2×3 matrix?
133)
A)
5
B)
3
C)
2
D)
1
Explain the mistake in the graph.
134)
x + y < –1
x – y 5
134)
A)
x – y 5 is shaded on the wrong side.
B)
x + y < –1 should be a dotted line.
C)
x + y < –1 is shaded on the wrong side.
D)
x – y 5 should be a dotted line.
27
Determine whether the system of equations is consistent with independent equations, consistent with dependent
equations, or inconsistent.
135)
5x – y = 23
x + 4y = 13
135)
A)
Consistent with dependent equations
B)
Consistent with independent equations
C)
Inconsistent
Solve the system of equations.
136)
9x + 8y = 4
3x – 6z = -8
4y – 3z = 6
136)
A)
– 2, 2, 2
3
B)
– 4
3, 2, 2
3
C)
4
3, 2, – 2
3
D)
2, – 4
3, 2
3
Describe the next row operation that should be performed to make the matrix closer to row echelon form.
137)
1 3 -15 -18
0 1 -14 21
0 4 2 –30
137)
A)
Replace R1 with – 3R2+R1.
B)
Replace R3 with -4R2+R3.
C)
Replace R3 with 1
4R3 .
D)
Replace R3 with 4R2+R3.
Solve by transforming the augmented matrix into row echelon form.
138)
2x + 5y – z = 37
x + 3y – 3z = 19
-5x + y + z = -13
138)
A)
no solution
B)
(4, 1, 6)
C)
(4, 6, 1)
D)
(-4, 6, 8)
Translate the problem to a system of equations, then solve using matrices.
139)
Mardi received an inheritance of $70,000. She invested part at 10% and deposited the remainder in
tax–free bonds at 8%. Her total annual income from the investments was $6400. Find the amount
invested at 10%.
139)
A)
$40,000
B)
$20,000
C)
$39,000
D)
$63,600
Solve the system using substitution.
140)
x + 7y = –7
5x + 8y = –35
140)
A)
no solution
B)
(–7, 0)
C)
(7, -1)
D)
all ordered pairs that solve x + 7y = –7
28
Translate to a system of two equations, then solve.
141)
Paul invested three times as much money in an account paying 5% interest than he did in an
account paying 4% interest. If the total interest paid was $475, how much did he invest in each?
141)
A)
$75 at 5%, $25 at 4%
B)
$7500 at 5%, $2500 at 4%
C)
$7500 at 5%, $3000 at 4%
D)
$2500 at 5%, $7500 at 4%
Determine whether the ordered triple is a solution of the system.
142)
(5, 2, -1)
2x + 3y + z = 15
5x – 4y – z = 18
3x + y + 2z = 15
142)
A)
Yes
B)
No
Translate the problem to a system of equations, then solve using matrices.
143)
A $114,000 trust is to be invested in bonds paying 6%, CDs paying 5%, and mortgages paying 9%.
The sum of the bond and CD investment must equal the mortgage investment. To earn an $8360
annual income from the investments, how much should the bank invest in bonds?
143)
A)
$36,000
B)
$38,000
C)
$19,000
D)
$57,000
Solve the system of equations.
144)
6x – 4y + 5z = -27
-18x + 12y – 15z = 81
12x – 8y + 10z = -54
144)
A)
(3, 5, –5)
B)
(– 3, – 5, 5)
C)
Infinite solutions
D)
No solution
Determine whether the given ordered pair is a solution to the given system of equations.
145)
(3, –2); 4x + y = 10
2x + 4y = –2
145)
A)
Yes
B)
No
Solve the system using elimination.
146)
6y = -4x – 8
2x – 3y = 8
146)
A)
no solution
B)
(0, -1)
C)
all ordered pairs that solve 2x – 3y =8
D)
(1, -2)
Determine whether the system of equations is consistent with independent equations, consistent with dependent
equations, or inconsistent.
147)
x + y = –3
2x – 2y = –3
147)
A)
Consistent with dependent equations
B)
Consistent with independent equations
C)
Inconsistent
29
Solve the system graphically.
148)
x = 1
y = 4
148)
A)
(4, 1)
B)
no solution
C)
(1, 4)
D)
(1, 1)
Translate the problem to a system of equations, then solve using matrices.
149)
A basketball fieldhouse seats 15,000. Courtside seats sell for $8, endzone for $6, and balcony for $5.
The total revenue from a sell–out is $86,000. If half the courtside and balcony seats and all the
endzone seats are sold, the total revenue is $49,000. How many of each type are there?
149)
A)
3200 courtside, 1800 endzone, 10,000 balcony
B)
3000 courtside, 3000 endzone, 8,000 balcony
C)
4000 courtside, 3000 endzone, 8000 balcony
D)
3000 courtside, 2000 endzone, 10,000 balcony
150)
Carole’s car averages 13.2 mi/gal in city driving and 25.8 mi/gal in highway driving. If she drove a
total of 518.4 mi on 24 gal of gas, how many of the gallons were used for city driving?
150)
A)
10 gal
B)
8 gal
C)
21 gal
D)
16 gal
Provide an appropriate response.
151)
When solving a system of equations, you get x + 5 = x + 5. How many solutions are there?
151)
A)
Infinitely many
B)
One solution
C)
No solutions
Determine whether the ordered triple is a solution of the system.
152)
(5, 4, -3)
x – y + z = 12
x + y + z = 6
x + y – z = -2
152)
A)
Yes
B)
No
30
Translate to a system of two equations, then solve.
153)
During a specific year, the percentage of high school sophomores that spent 13 hours or more each
week preparing for class was 13% more than those that spent less than 13 hours preparing for class.
If the percentage of both groups totals 100%, what percentage of high school sophomores spent 13
hours or more each week preparing for class?
153)
A)
43.5% spent 13 hr or more, 56.5% spent less than 13 hr
B)
42.5% spent 13 hr or more, 57.5% spent less than 13 hr
C)
56.5% spent 13 hr or more, 43.5% spent less than 13 hr
D)
57.5% spent 13 hr or more, 42.5% spent less than 13 hr
Graph the solution of the system.
154)
2x + y 4
y – 1 0
154)
A)
B)
C)
D)
31
Determine whether the given ordered pair is a solution to the given system of equations.
155)
(4, -6); 4x – y = -22
2x – 4y = -32
155)
A)
Yes
B)
No
156)
(-3, -6); x + y = -9
x – y = 3
156)
A)
Yes
B)
No
Translate into a system of equations. Do not solve.
157)
The difference between two numbers is 1. Three times the smaller number plus the larger number
is 97. What are the numbers? (Let x represent the larger number and y represent the smaller
number.)
157)
A)
x – y = 1
x + 3z = 97
B)
x – y = 1
3x + y = 97
C)
x – y = 1
x + 3y = 97
D)
x + y = 1
x + 3y = 97
Translate to a system of two equations, then solve.
158)
The supplement of an angle measures 26° more than twice its complement. Find the measure of the
angle.
158)
A)
128°
B)
52°
C)
38°
D)
26°
Translate to a system of three equations, then solve.
159)
The sum of three numbers is -5. The first, minus the second, plus 3 times the third, is 15. The third,
plus 2 times the first, plus the second, is -10. What are the numbers?
159)
A)
-5, -5, –5
B)
5, 5, –5
C)
-5, –5, 5
D)
No solution
Solve the system graphically.
160)
6x + y = 26
6x + y = 56
160)
A)
no solution
B)
(24, 2)
C)
all ordered pairs that solve 6x + y =56
D)
(22, -106)
32
Complete the indicated row operation.
161)
Replace R2 in -4 4 -1
–52 0 with 5R2.
161)
A)
-20 20 –5
–52 0
B)
-4 4 1
–25 10 0
C)
-4 4 1
-20 20 –5
D)
-20 20 –5
–25 10 0
162)
Replace R2 in –76 1
-4 0 9 with -4R1+R2.
162)
A)
–76 1
24 -24 5
B)
–76 1
-32 24 13
C)
24 -24 5
-4 0 9
D)
–76 1
-11 610
Solve the system graphically.
163)
x – y = 2
x + y = 10
163)
A)
(4, 6)
B)
(12, 8)
C)
(6, 4)
D)
(8, 12)
Solve by transforming the augmented matrix into row echelon form.
164)
9x – y + 6z = 41
–2x + 5y + 7z = 66
9x – 6y + z = -19
164)
A)
(2, 7, 5)
B)
(-2, 7, 4)
C)
(2, 5, 7)
D)
no solution
Translate to a system of two equations, then solve.
165)
If a plane can travel 230 miles per hour with the wind and only 170 miles per hour against the
wind, find the speed of the wind and the speed of the plane in still air.
165)
A)
Plane: 300 mph, wind: 30 mph
B)
Plane: 200 mph, wind: 30 mph
C)
Plane: 30 mph, wind: 200 mph
D)
Plane: 200 mph, wind: 40 mph
Provide an appropriate response.
166)
Solving for which variable in which equation involves the least amount of work?
3x =6
x – 9y =29
166)
A)
x in equation 1
B)
y in equation 1
C)
y in equation 2
D)
x in equation 2
33
Solve using a matrix on a graphing calculator.
167)
9x + 2y – z = 10
x – 5y – 5z = -24
-8x + y + z = -3
167)
A)
(1, 3, 2)
B)
(-1, 2, 2)
C)
(1, 2, 3)
D)
No solution
Solve the system using elimination.
168)
x + 3y = 13
–5x + 3y = 43
168)
A)
(-6, -5)
B)
(-5, 6)
C)
no solution
D)
(-4, 5)
Indicate whether the statement is true or false.
169)
When graphing a linear inequality, the origin can always be used as a test point for determining
which side of a boundary line should be shaded.
169)
A)
True
B)
False
Determine whether the ordered triple is a solution of the system.
170)
(4, –5, -4)
x + y + z = –5
x – y + 5z = -11
4x + y + z = 7
170)
A)
Yes
B)
No
Solve the system using substitution.
171)
5x + y = 4
-20x – 4y = -16
171)
A)
(0, 4)
B)
(5, 0)
C)
no solution
D)
all ordered pairs that solve 5x + y =4
Describe the next row operation that should be performed to make the matrix closer to row echelon form.
172)
1-14 20
–15 -7 14
172)
A)
Replace R2 with – 1
7R2.
B)
Replace R2 with 15R1+R2.
C)
Replace R2 with –15R1+R2.
D)
Replace R2 with –1
15R2.
34
Complete the indicated row operation.
173)
Replace R2 in 2611 1
7–712 12
-1 –3–6 0 with 5R2.
173)
A)
2611 1
12 –217 17
-1 –3–6 0
B)
230 11 1
7–35 12 12
-1 –15 –6 0
C)
2611 1
35 –35 60 60
-1 –3–6 0
D)
10 30 55 5
35 –35 60 60
-5 –15 –30 0
Translate to a system of three equations, then solve.
174)
A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1
black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. They used 100 black, 110 white and
90 red wires. How many of each cable were made?
174)
A)
20 cable A, 30 cable B, 10 cable C
B)
10 cable A, 30 cable B, 93 cable C
C)
10 cable A, 30 cable B, 20 cable C
D)
10 cable A, 103 cable B, 20 cable C
Translate the problem to a system of equations, then solve using matrices.
175)
A grain dealer sold to one customer 5 bushels of wheat, 2 of corn, and 3 of rye, for $20.60; to
another, 2 of wheat, 3 of corn, and 5 of rye, for $28.40; and to a third, 3 of wheat, 5 of corn, and 2 of
rye, for $22.10. What was the price per bushel for corn?
175)
A)
$4.20
B)
$2.36
C)
$2.10
D)
$1.60
Translate to a system of two equations, then solve.
176)
How many liters of a 30% alcohol solution must be mixed with 40 liters of a 70% solution to get a
50% solution?
176)
A)
4 L
B)
80 L
C)
8 L
D)
40 L
177)
There were 420 people at a play. The admission price was $3 for adults and $1 for children. The
admission receipts were $780. How many adults and how many children attended?
177)
A)
180 adults and 240 children
B)
240 adults and 180 children
C)
195 adults and 225 children
D)
120 adults and 300 children
Solve the system using substitution.
178)
9x – 5y = 25
7x – 2y = 10
178)
A)
(0, -4)
B)
no solution
C)
(-1, -4)
D)
(0, -5)
Solve by transforming the augmented matrix into row echelon form.
179)
x + y + z = -3
x – y + 4z = 16
3x + y + z = -5
179)
A)
(3, -5, -1)
B)
no solution
C)
(-1, -5, 3)
D)
(3, -1, -5)
35
Graph the solution of the system.
180)
x + 2y 2
x + y 0
180)
A)
B)
C)
D)
Translate into a system of equations. Do not solve.
181)
The perimeter of a rectangular building is 136 feet. The width is 2 feet shorter than the length. What
are the dimensions? (Let W represent the width and L represent the length.)
181)
A)
L = W – 2
2L + W = 136
B)
W = L + 2
2L + 2W = 136
C)
W = L – 2
L + W = 136
D)
W = L – 2
2L + 2W = 136
36
Graph the solution of the system.
182)
3x – 2y 6
x – 1 0
182)
A)
B)
C)
D)
Solve the system using substitution.
183)
5x – 55 = –7y
-2x + 2y = 2
183)
A)
(3, 6)
B)
all ordered pairs that solve -2x + 2y =2
C)
no solution
D)
(4, 5)
Solve the problem.
37
184)
Bruce is a retired carpenter who builds patio chairs and dog houses which he sells at his local flea
market. It takes him 4 hours to build a dog house and 5 hours to build a patio chair. Bruce can work
no more than 40 hours per week and he must produce more dog houses than chairs. Write a system
of inequalities to describe this situation and solve the system by graphing. Use D for the number of
dog houses and P for the number of patio chairs produced in a week.
184)
A)
B)
C)
D)
38
Solve using a matrix on a graphing calculator.
185)
4x + 3y – z = 35
x – 5y – 2z = -19
-5x + y + z = -31
185)
A)
(8, 3, 6)
B)
(-8, 3, 16)
C)
(8, 6, 3)
D)
No solution
Determine whether the system of equations is consistent with independent equations, consistent with dependent
equations, or inconsistent. How many solutions does the system have?
186)
186)
A)
Consistent with dependent equations; infinite number of solutions
B)
Consistent with independent equations; one solution
C)
Inconsistent; no solution
Determine whether the given ordered pair is a solution to the given system of equations.
187)
2
3, – 1
3; 6x – 3y = 6
-18x + 9y = -24
187)
A)
Yes
B)
No
Translate to a system of three equations, then solve.
188)
A croissant, a cup of coffee, and a fruit bowl from Kelley’s Coffee Cart cost a total of $5.50, and a
croissant costs twice as much as a cup of coffee. Kelley posts a notice announcing that, effective
next week, the price of a croissant will go up 10% and the price of coffee will go up 15%. After the
increase, the total price of the purchase will be $5.76. Find the cost of each item before the increase.
188)
A)
A fruit bowl costs $3.25, a croissant costs $0.86, and a cup of coffee costs $1.65.
B)
A fruit bowl costs $3.25, a croissant costs $1.50, and a cup of coffee costs $0.75.
C)
A fruit bowl costs $3.25, a croissant costs $1.65, and a cup of coffee costs $0.86.
D)
The prices cannot be determined from the given information.
Indicate whether the statement is true or false.
189)
Every system of two linear inequalities has infinitely many solutions.
189)
A)
True
B)
False
39
Graph the solution of the system.
190)
3x + 2y -6
x – 1 0
190)
A)
B)
C)
D)
40
191)
x – 2y 2
x + y 0
191)
A)
B)
C)
D)
41
Answer Key
Testname: C4
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Answer Key
Testname: C4
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Answer Key
Testname: C4
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Answer Key
Testname: C4
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