Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
41)
5y =42 –4x
2x =46 –5y
41)
A)
{(5, –10)}
B)
{(–2, 10)}
C)
{(x, y) 4x +5y =42 }
D)
Determine whether the given ordered pair is a solution of the system.
42)
(1, –4)
x + y = – 5
x – y =3
42)
A)
solution
B)
not a solution
B
Graph the solution set of the system of inequalities or indicate that the system has no solution.
43)
y >x2
10x +3y 30
43)
A)
B)
21
B
C)
D)
Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
44)
4x – 3y =8
–8x + 6y = – 32
44)
A)
1
6, –1
8
B)
{(2, 4)}
C)
{(x, y)| 4x – 3y =8}
D)
An objective function and a system of linear inequalities representing constraints are given. Graph the system of
inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region.
Use these values to determine the maximum value of the objective function and the values of x and y for which the
maximum occurs.
45)
Objective Function z = 6x + 7y
Constraints x 0
y 0
2x + 3y 12
2x + y
8
45)
A)
Maximum 32; at (2, 3)
B)
Maximum 32; at (3, 2)
C)
Maximum 52; at (4, 4)
D)
Maximum 24; at (4, 0)
22
Decide if the system of equations in two variables is linear or nonlinear.
46)
x2=2y +4
8x – y =7
46)
A)
Nonlinear
B)
Linear
Write the partial fraction decomposition of the rational expression.
47)
8x2–8x +5
(x– 1)3
47)
A)
8
x – 1 +8
(x– 1)2
B)
8
x – 1 –8
(x– 1)2+5
(x– 1)3
C)
8
x – 1 +x +8
(x– 1)2+x2+5
(x– 1)3
D)
8
x – 1 +8
(x– 1)2+5
(x– 1)3
Decide if the system of equations in two variables is linear or nonlinear.
48)
x3+3x= y
x +7y =3
48)
A)
Linear
B)
Nonlinear
Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
49)
x + 3y = – 2
2x + 6y = – 4
49)
A)
{(–2, 0)}
B)
{(0, 0)}
C)
{(x, y) | x + 3y = – 2}
D)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
23
Explanation:
50)
2x + 3y 6
x – y 3
y 2
50)
A)
B)
C)
D)
24
Determine if the given ordered triple is a solution of the system.
51)
(1, –1, 0)
x – y + 4z =5
4x + z =1
x + 2y + z = – 1
51)
A)
solution
B)
not a solution
Find the maximum or minimum value of the given objective function of a linear programming problem. The figure
illustrates the graph of feasible points.
52)
Objective Function: z = x + 9y + 7
Find minimum.
52)
A)
minimum: 29
B)
minimum: 38
C)
minimum: 54
D)
no minimum
Solve the system of equations by the substitution method.
53)
–2x – 3y= – 21
x= – 5y
53)
A)
{(–3, 15)}
B)
{(16, –3)}
C)
{(15, –3)}
D)
{(15, 3)}
Solve the system by the addition method.
54)
2x +6y = – 16
–2x –10y=28
54)
A)
{(–1, 3)}
B)
{(–1, –3)}
C)
{(1, –3)}
D)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
25
55)
y 3x
y 8
55)
A)
B)
C)
D)
Solve the problem.
56)
Three shrimp boats supply the shrimp wholesalers on Hilton Head with fresh catch. The Annabelle
takes 50% of its catch to Hudson’s, 20% to Captain J’s, and 30% to Mainstreet. The Curly Q takes
40% of its catch to Hudson’s, 40% to Captain J’s, and 20% to Mainstreet. The SloJoe takes 30% of its
catch to Hudson’s, 40% to Captain J’s, and 30% to Mainstreet. One week Hudson’s received 238.4
pounds of shrimp, Captain J’s received 212.4 pounds, and Mainstreet received 156.2 pounds. How
many pounds of shrimp did each boat catch?
56)
A)
Annabelle 196 lbs, Curly Q 259 lbs, SloJoe 152 lbs
B)
Annabelle 259 lbs, Curly Q 196 lbs, SloJoe 152 lbs
C)
Annabelle 152 lbs, Curly Q 259 lbs, SloJoe 196 lbs
D)
Annabelle 196 lbs, Curly Q 152 lbs, SloJoe 259 lbs
Determine whether the given ordered pair is a solution of the system.
57)
(–6, 2)
4x = – 22 – y
2x = – 4– 4y
57)
A)
solution
B)
not a solution
A
Determine if the given ordered triple is a solution of the system.
58)
(5, 1, 2)
x + 2y + 5z =17
2y + 2z =6
z =2
58)
A)
not a solution
B)
solution
B
Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
59)
x – 6y =13
2x – 7y =21
59)
A)
{(6, 0)}
B)
{(7, –1)}
C)
{(x, y) x – 6y =13}
D)
B
Graph the inequality.
27
C
60)
x – y > – 2
60)
A)
B)
C)
D)
Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
61)
x
3+y
6= 1
x
4–y
8= 0
61)
A)
3
2, 3
B)
3, 3
2
C)
(x, y) x
3+y
6= 1
D)
Solve the problem.
62)
In 1985, in the town of Appleby, 21.2% of Hispanics were overweight, increasing by an average of
0.41% per year. In 1985, in the town of Appleby, 0.16% of whites were overweight, increasing by
an average of 29.0% per year. Write a function that models the percentage, y, of Hispanics who are
overweight x years after 1985. Write a function that models the percentage, y, of whites who are
overweight x years after 1985.
62)
A)
Hispanics: y +0.41x =21.2
Whites: y +29.0x =0.16
B)
Hispanics: y =21.2x +0.41
Whites: y =0.16x +29.0
C)
Hispanics: y =0.41x +21.2
Whites: y =29.0x +0.16
D)
Hispanics: y =21.61x
Whites: y =29.16x
Graph the solution set of the system of inequalities or indicate that the system has no solution.
63)
(x + 5)2+(y + 2)2>16
(x + 5)2+(y + 2)2< 36
63)
29
A)
B)
C)
D)
Solve the problem.
64)
Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks.
This time it is all nickels and dimes. There are 5 times as many dimes as nickels, and the value of
the dimes is $4.50 more than the value of the nickels. How many nickels and dimes does Jamil
have?
64)
A)
9 nickels and 45 dimes
B)
50 nickels and 10 dimes
C)
11 nickels and 55 dimes
D)
10 nickels and 50 dimes
Determine if the given ordered triple is a solution of the system.
65)
(0, –4, –3)
x – y + 5z = – 11
2x + z = – 3
x + 5y+ z = – 23
65)
A)
solution
B)
not a solution
Graph the inequality.
66)
y x2+ 2
66)
A)
B)
C)
D)
31
Solve the problem.
67)
A man is planting a section of garden with tomatoes and cucumbers. The available area of the
section is 150 square feet. He wants the area planted with tomatoes to be more than 25% of the area
planted with cucumbers. Write a system of inequalities to describe the situation. Let x = amount to
be planted in tomatoes and y = amount to be planted in cucumbers.
67)
A)
x + y 150
0.25x > y
x 0
y 0
B)
x + y 150
x <0.25y
x 0
y 0
C)
x + y =150
x 0.25y
x 0
y 0
D)
x + y 150
x >0.25y
x 0
y 0
Graph the solution set of the system of inequalities or indicate that the system has no solution.
68)
x2+y236
x2+y21
68)
A)
no solution
B)
C)
D)
32
Graph the inequality.
69)
2x + y –5
69)
A)
B)
C)
D)
33
An objective function and a system of linear inequalities representing constraints are given. Graph the system of
inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region.
Use these values to determine the maximum value of the objective function and the values of x and y for which the
maximum occurs.
70)
Objective Function z =17x – 20y
Constraints 0 x
5
0 y 8
4x + 5y 30
4x + 3y 20
70)
A)
Maximum: –120; at (0, 6)
B)
Maximum: –78.75; at (1.25, 5)
C)
Maximum: 85; at (5, 0)
D)
Maximum: 0; at (0, 0)
Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
71)
3x + 4
(x2+ x + 5)2
71)
A)
A
x2+ x + 5
+Bx + C
(x2+ x + 5)2
B)
Ax + B
x2+ x + 5
+Cx + D
(x2+ x + 5)2
C)
A
x2+ x + 5
+B
(x2+ x + 5)2
D)
Ax + B
x2+ x + 5
+C
(x2+ x + 5)2
Solve the problem.
72)
The diagonal of the floor of a rectangular office cubicle is 2 ft longer than the length of the cubicle
and 5 ft longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth,
if necessary.
72)
A)
width = 4 ft, length = 11 ft
B)
width = 9.7 ft, length = 22.4 ft
C)
width = 2 ft, length = 9 ft
D)
width = 3.9 ft, length = 9.7 ft
Graph the inequality.
34
73)
x
4+y
3 1
73)
A)
B)
C)
D)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
35
74)
x2+y281
5x + 2y 10
74)
A)
B)
C)
D)
36
Solve the problem.
75)
Three trains one eastbound, one westbound, and one northbound leave a city at the same time.
The speed of the northbound train is 30 miles per hour greater than the speed of the eastbound
train. After 2 hours, the distance between the westbound train and the eastbound train is 160 miles.
Twice the speed of the westbound train is 40 miles per hour more than the speed of the northbound
train. Find the speeds of the three trains.
75)
A)
eastbound, 40 mph; westbound, 50 mph; northbound, 70 mph
B)
eastbound, 20 mph; westbound, 60 mph; northbound, 60 mph
C)
eastbound, 60 mph; westbound, 50 mph; northbound, 30 mph
D)
eastbound, 30 mph; westbound, 50 mph; northbound, 60 mph
Determine whether the given ordered pair is a solution of the system.
76)
(–4, –2)
4x + y = – 14
2x + 4y =0
76)
A)
solution
B)
not a solution
Solve the problem.
77)
The following is known about three numbers: If the second number is subtracted from the sum of
the first number and 4 times the third number, the result is 13. The third number plus 2 times the
first number is 4. The first number plus 5 times the second number plus the third number is 19.
Find the three numbers.
[Hint: let x represent the first number, y the second number, and z the third number. Use the given
conditions to write and solve a system of equations.]
77)
A)
x =0, y =2, z =9
B)
x = – 1, y =3, z =6
C)
x =0, y =3, z =4
D)
x =1, y =4, z =4
Determine if the given ordered triple is a solution of the system.
78)
(2, 5, –3)
x + y + z =4
x – y + 3z = – 2
2x + y + z =1
78)
A)
not a solution
B)
solution
Solve the problem.
79)
A flat rectangular piece of aluminum has a perimeter of 56 inches. The length is 12 inches longer
than the width. Find the width.
79)
A)
20 inches
B)
28 inches
C)
8 inches
D)
32 inches
Solve the system by the addition method.
80)
x2+y2=164
x2–y2=36
80)
A)
{(10, –8), (10, 8)}
B)
{(10, 8), (–10, 8), (10, –8), (–10, –8)}
C)
{(10, 8), (8, 10), (–10, –8), (–8, –10)}
D)
{(–10, –8), (–8, –10)}
Write the partial fraction decomposition of the rational expression.
81)
5x2+ 7x + 4
x3+ 3x2+ 5x + 15
81)
A)
2
x + 3 +3x – 2
x2+ 5
B)
2
x + 3 +3
x2+ 5
C)
2
x + 3 +3
x + 5 +
–2
(x + 5)2
D)
2
x + 5 +3x – 2
x2+ 3
Graph the solution set of the system of inequalities or indicate that the system has no solution.
82)
2x + y >4
2x + y <1
82)
38
A)
B)
C)
D)
no solution
Decide if the system of equations in two variables is linear or nonlinear.
83)
x =5y +9
5x – y =2
83)
A)
Linear
B)
Nonlinear
Solve the problem.
84)
The Family Fine Arts Center charges $20 per adult and $10 per senior citizen for its performances.
On a recent weekend evening when 511 people paid admission, the total receipts were $7020. How
many who paid were senior citizens?
84)
A)
281 senior citizens
B)
320 senior citizens
C)
230 senior citizens
D)
191 senior citizens
Explanation:
Solve the system of equations by the substitution method.
85)
–9x + y =5
–3x – 4y = – 7
85)
A)
–1
3, 2
B)
2
3, 11
C)
–4, –3
2
D)
{(1, –1)}
Graph the inequality.
86)
–2x – 5y –10
86)
A)
B)
C)
D)