Solve the system. If there is no solution or if the system‘s equations are dependent, so state.
57)
x–y+2z =5
4x +z=0
x+4y +z= – 20
57)
A)
{(0, –5, 0)}
B)
infinitely many solutions; dependent equations
C)
{(0, 0, –5)}
D)
no solution or
Solve the system by the best method. Use set notation to express the solution set.
58)
x + 8y = 0
x – 8y =32
58)
A)
{(–2, 16)}
B)
{(8, –1)}
C)
{(16, –2)}
D)
{(16, 2)}
Determine if the given ordered triple is a solution of the system.
59)
59)
(0, 2, –5)
x – y + 3z = – 17
2x + z = – 5
x + 2y + z = – 1
A)
solution
B)
not a solution
Determine whether the ordered pair is a solution of the system.
60)
60)
(3, –1)
x + y =2
x – y =4
A)
Yes
B)
No
Solve the problem.
61)
61)
If $2000 is invested at 10% annual interest, how much should be invested at 12% annual interest
so that the total yearly income from both investments is $5000?
A)
$4760
B)
$40,000
C)
$4000
D)
$47,600
Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
62)
x + 4y =36
8x + 5y =45
62)
A)
{(–9, 0)}
B)
{(0, 9)}
C)
no solution;
D)
{(1, 8)}
Solve the system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
63)
y =2x + 4
4x + y = – 8
63)
A)
{(0, –8)}
B)
{(–3, –2)}
C)
{(–2, 0)}
D)
{(0, –2)}
Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
64)
x + y = – 2
x – y =6
64)
A)
no solution;
B)
{(–4, 2)}
C)
{(2, –4)}
D)
{(2, 4)}
Solve the problem.
65)
65)
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 9 times as many dimes as nickels, and the
value of the dimes is $5.95 more than the value of the nickels. How many nickels and dimes does
Jamil have?
A)
8 nickels and 72 dimes
B)
7 nickels and 63 dimes
C)
63 nickels and 7 dimes
D)
6 nickels and 54 dimes
Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
66)
x – 3y = – 3
2x + 3y =12
66)
A)
no solution;
B)
{(3, –2)}
C)
{(2, 3)}
D)
{(3, 2)}
Solve the system. If there is no solution or if the system‘s equations are dependent, so state.
67)
x–2y –z= – 2
–3x +6y +3z =6
4x –8y –4z = – 8
67)
A)
{(4, –3, 12)}
B)
no solution or
C)
{(–3, 4, –9)}
D)
infinitely many solutions; dependent equations
Solve the problem.
68)
68)
Melissa invested a sum of money at 3% annual interest. She invested three times that sum at 5%
annual interest. If her total yearly interest from both investments was $5400, how much was
invested at 3%?
A)
$22,500
B)
$67,500
C)
$202,500
D)
$30,000
Determine if the given ordered triple is a solution of the system.
69)
69)
(–3, 4, 1)
3x + 3y + z =4
4x – 4y – z = – 29
2x + y + 4z =2
A)
solution
B)
not a solution
Solve the problem.
70)
70)
A twin–engined aircraft can fly 1360 miles from city A to city B in 5 hours with the wind and
make the return trip in 8 hours against the wind. What is the speed of the wind?
A)
68 mph
B)
34 mph
C)
85 mph
D)
51 mph
71)
71)
Sybil is having her yard landscaped. She obtained an estimate from two landscaping companies.
Company A gave an estimate of $240 for materials and equipment rental plus $55 per hour for
labor. Company B gave an estimate of $320 for materials and equipment rental plus $45 per hour
for labor. We can represent this situation with the system of linear equations
c =240 +55xCompany A
c =320 +45xCompany B
where c is the total cost and x is the number of hours of labor.
Graph the system. What is the x–coordinate of the intersection point of the graphs? Describe what
this x–coordinate means in practical terms.
A)
7; there is a number of hours of labor, for which both companies charge $700.
B)
7; for 7 hours of labor, both companies charge the same.
C)
11; for 11 hours of labor, both companies charge the same.
D)
8; for 8 hours of labor, both companies charge the same.
Solve the system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
72)
y – 6x =4
4y =24x + 16
72)
A)
no solution;
B)
infinitely many solutions; {(x, y) y – 6x =4} or {(x, y) 4y =24x + 16}
C)
{(–1.5, –1)}
D)
{(1, 1)}
Solve the system by the best method. Use set notation to express the solution set.
73)
–2x – 8y = – 38
6x – 9y = – 18
73)
A)
{(2, 5)}
B)
{(–3, 5)}
C)
no solution;
D)
{(3, 4)}
Determine if the given ordered triple is a solution of the system.
74)
74)
(–5, 4, –3)
x + 4y + 5z = – 12
3y + 4z = – 8
z = – 5
A)
not a solution
B)
solution
Solve the problem.
75)
75)
How can $28,000 be invested, part at 4% annual interest and the remainder at 10% annual
interest, so that the interest earned by the two accounts is equal at the end of the year?
A)
$20,000 invested at 4%; $8000 invested at 10%
B)
$10,000 invested at 4%; $18,000 invested at 10%
C)
$8000 invested at 4%; $20,000 invested at 10%
D)
$18,000 invested at 4%; $10,000 invested at 10%
Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
76)
4 x – y =20
3x + y =22
76)
A)
{(4, 6)}
B)
no solution;
C)
{(6, 4)}
D)
{(6, 5)}
Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
77)
4x + 4y =36
2x – 2y =2
77)
A)
{(4, –6)}
B)
no solution;
C)
{(4, 5)}
D)
{(5, 4)}
Solve the problem.
78)
78)
The sum of two numbers is –5. Three times the first number equals 2 times the second number.
Find the two numbers.
A)
2 and 3
B)
–10 and –15
C)
–5 and 6
D)
– 2 and – 3
79)
79)
A tour group split into two groups when waiting in line for food at a fast food counter. The first
group bought 8 slices of pizza and 4 soft drinks for $34.72. The second group bought 5 slices of
pizza and 5 soft drinks for $26.50. How much does one slice of pizza cost?
A)
$3.38 per slice of pizza
B)
$2.88 per slice of pizza
C)
$1.92 per slice of pizza
D)
$2.42 per slice of pizza
Solve the system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to
express the solution set.
80)
3x + y = – 11
4x + 2y = – 12
80)
A)
{(5, 4)}
B)
{(–3, –2)}
C)
{(–5, –6)}
D)
{(–5, 4)}
Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
81)
x + y =8
x + y =4
81)
A)
{(0, 0)}
B)
{(8, 4)}
C)
no solution;
D)
{(0, 12)}
Solve the system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
82)
1
2x +1
2y = – 1
x – y =4
82)
A)
{(1, –3)}
B)
{(–1, –2)}
C)
{(0, –2)}
D)
no solution;
29
Solve the problem.
83)
83)
A company’s cost for producing x magazines is given by the equation y = x + 1500. The revenue
for selling x magazines is given by the equation y = 3x. The break–even point is the point at
which the cost and revenue are the same. The graphs of the two equations are shown. Use the
graph to solve the system.
y = x +
1500
y = 3x
Interpret the coordinates of the solution in practical terms.
A)
{(650, 2150)}; If 650 magazines are produced and sold, the company will break even: both
cost and revenue will be equal to $2150.
B)
{(750, 2250)}; If 750 magazines are produced and sold, the company will break even: both
cost and revenue will be equal to $2250.
C)
{(750, 2250)}; If 2250 magazines are produced and sold, the company will break even: both
cost and revenue will be equal to $750.
D)
{(750, 2400)}; If 750 magazines are produced and sold, the company will break even: both
cost and revenue will be equal to $2400.
84)
84)
Khang and Hector live 27 miles apart in southeastern Missouri. They decide to bicycle towards
each other and meet somewhere in between. Hector’s rate of speed is 80% of Khang’s. They start
out at the same time and meet 3 hours later. Find Hector’s rate of speed.
A)
4 mph
B)
15 mph
C)
5 mph
D)
27 mph
Determine whether the system is inconsistent, dependent, or neither.
85)
x + y + z =10
x – y + 2z =9
2x +2y + 2z =15
85)
A)
dependent
B)
inconsistent
C)
neither
Solve the system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set
notation to express the solution set.
86)
x = – y
x + y = 6
86)
A)
{(1, 1)}
B)
infinitely many solutions; {(x, y) x + y = 6} or {(x, y) x = – y}
C)
no solution;
D)
{(1, 5)}
87)
3x + y =14
12x + 4y =56
87)
A)
{(5, –1)}
B)
{(0, 14)}
C)
infinitely many solutions; {(x, y) 3x + y =14} or {(x, y) 12x + 4y =56}
D)
no solution;
Determine whether the ordered pair is a solution of the system.
88)
88)
(5, –3)
4x + y =17
3x + 4y =3
A)
not a solution
B)
solution
Solve the problem.
89)
89)
A deli sells three sizes of turkey sandwiches: the small turkey sandwich contains 5 ounces of meat
and sells for $2.50; the regular turkey sandwich contains 8 ounces of meat and sells for $3.00; and
the large turkey sandwich contains 10 ounces of meat and sells for $3.50. A customer requests a
selection of each size for a reception. She and the manager agree on a combination of 40
sandwiches made from 18 pounds 10 ounces of turkey for a total cost of $115. How many of each
size sandwich will be in this combination? (Note: 1 pound = 16 ounces)
A)
18 small sandwiches, 14 medium sandwiches, 8 large sandwiches.
B)
14 small sandwiches, 10 medium sandwiches, 16 large sandwiches.
C)
20 small sandwiches, 8 medium sandwiches, 12 large sandwiches.
D)
16 small sandwiches, 20 medium sandwiches, 4 large sandwiches.
90)
90)
On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of
bracelets at $6 each and a number of necklaces at $12 each. She wrote a check for $1140 to pay for
the order. How many bracelets and how many necklaces did Rosaria purchase?
A)
45 bracelets and 75 necklaces
B)
60 bracelets and 60 necklaces
C)
55 bracelets and 65 necklaces
D)
50 bracelets and 70 necklaces
Solve the system by the best method. Use set notation to express the solution set.
91)
8x + 98 =6y
–3x – 4y = – 7
91)
A)
{(–7, 8)}
B)
no solution;
C)
{(–8, 8)}
D)
{(–7, 7)}