Deck 7: Systems and Matrices

Question 1

Solve the system by substitution.
x + 5y = 11 -2x - 10y = -12

A) No solution
B) (1, 1)
C) (1, 2)
D) (2, 2)

Answer 1

A

Question 2

Solve the system algebraically.

Answer 2

A

Question 3

Solve the system by substitution.
x + 9y = 9 -4x + 10y = 10

A) (-1, 0)
B) (0, 1)
C) (1, 0)
D) No solution

Answer 3

B

Question 4

Solve the system by substitution.

Question 5

Solve the system by substitution.
x - 5y = -1 y = 1

A) (-4, 1)
B) (-6, 1)
C) (4, 1)
D) (1, 4)

Question 6

Solve the system by substitution.
x + 6y = 0 x - 6y = 96

A) (-8, 48)
B) (6, -1)
C) (48, -8)
D) (48, 8)

Question 7

Solve the system by substitution.
x + 3y = 15 2x + 3y = 24

A) (10, 1)
B) (10, 9)
C) No solution
D) (9, 2)

Question 8

Question 9

Solve the system by substitution.

Question 10

Solve the system by substitution.
x + y = 3 x - y = 1

A) (2, 1)
B) No solution
C) (1, 2)
D) (-2, 2)

Question 11

Solve the system by substitution.
x - 7y = -56 9x - 7y = -112

A) No solution
B) (-6, 6)
C) (-7, 7)
D) (7, 6)

Question 12

(1, -6) x + y = -5
X - y = 7

A) No
B) Yes

Question 13

Solve the system algebraically.

Question 14

Question 15

Solve the system by substitution.
x + 6y = 9 -2x + 5y = -1

A) (-3, 2)
B) (3, 1)
C) No solution
D) (2, 2)

Question 16

(4, 5) 4x + y = 11
2x + 4y = -12

A) Yes
B) No

Question 17

(-1, 4) x + y = 5
X - y = -3

A) No
B) Yes

Question 18

Question 19

(6, 2) 3x + y = 20
4x + 3y = 30

A) No
B) Yes

Question 20

Solve the system algebraically.

Question 21

Solve the system by elimination.
-x + 2y = -3 2x - 4y = 6

A) (2y - 3, y)
B) (3, 0)
C) (2y + 3, y)
D) (0, - 32 )

Question 22

Solve the system by elimination.
8x - 3y = 22 3x + 8y = 63

A) (5, 6)
B) No solution
C) (-2, -7)
D) (-5, 6)

Question 23

Solve the system by elimination.

Question 24

Solve the system by elimination.
2x + y = 9 x - 2y = 2

A) (6, 2)
B) (5, -1)
C) (3, 1)
D) (4, 1)

Question 25

Solve the system by elimination.
-7x - 4y = -12 -3x - 2y = -6

A) (0, 3)
B) (0, 4)
C) No solution
D) (-1, 4)

Question 26

Use the graph to estimate any solutions of the system.

Question 27

Solve the system algebraically.

Question 28

Solve the system by elimination.
x - 3y = -21 5x - 2y = -14

A) (-7, 0)
B) No solution
C) (0, 7)
D) (1, 6)

Question 29

Use the graph to estimate any solutions of the system.

Question 30

Use the graph to estimate any solutions of the system.

Question 31

Solve the system algebraically.

Question 32

Solve the system by elimination.
6x - 4y = 40 -3x - 2y = -4

A) No solution
B) (4, -3)
C) (3, -3)
D) (4, -4)

Question 33

Solve the system by elimination.
-4x + 9y = -71 -8x = -73 - 18y

A) (2, 10)
B) (2, -7)
C) (8, 10)
D) No solution

Question 34

Use the graph to estimate any solutions of the system.

Question 35

Solve the system algebraically.

Question 36

Solve the system by elimination.
-7x - 7y = -49 -3x + 4y = -21

A) No solution
B) (7, 1)
C) (6, 1)
D) (7, 0)

Question 37

Use the graph to estimate any solutions of the system.

Question 38

Solve the system by elimination.
6x - 44 = 8y 4x - 6y = 30

A) (5, 0)
B) (6, 0)
C) No solution
D) (6, -1)

Question 39

Use a graph to determine the number of solutions the system has.

Question 40

Use the graph to estimate any solutions of the system.

Question 41

Solve the system graphically.

Question 42

Use a graph to determine the number of solutions the system has.

Question 43

Solve the system graphically.

Question 44

Solve the system graphically.

- $x^{2}+y^{2}=7$
$y=\sqrt[3]{x+6}$

A) $\approx(-2,13,157) \text { and } \approx(1,76 \cdot 1.98)$
B) $\approx(-1.76,-1.98) \text { and } \approx(2.13,-1.57)$
C) $\approx(-2.13,-1.57) \text { and } \approx(1.76,-1.98)$
D) $\approx(-2.29,-1.32) \text { and } \approx(2.29,1.32)$

Question 45

Solve the system graphically.

Question 46

Solve the problem.
The total number of cars sold at a used car lot for the years 1996 and 1997 was 1184. From 1996 to 1997 the number of cars sold declined by 158. How many cars were sold in 1996?

A) 659
B) 671
C) 677
D) 649

Question 47

Use a graph to determine the number of solutions the system has.
2x - 2y = -4 3x + 3y = -12

A) One solution
B) No solution
C) Infinitely many solutions

Question 48

Solve the system graphically.

Question 49

Solve the system graphically.

Question 50

Use a graph to determine the number of solutions the system has.

Question 51

Solve the system graphically.

Question 52

Solve the problem.
A theatre sells two types of tickets to their plays; children's tickets and adult tickets. For today's performance they have sold a total of 1120 tickets. Also, they have sold 4 times as many adult tickets as children's tickets.
How many adult tickets have they sold?

A) 902
B) 889
C) 893
D) 896

Question 53

Use a graph to determine the number of solutions the system has.

Question 54

Solve the problem.
A theatre sells two types of tickets to their plays; children's tickets and adult tickets. For today's performance they have sold a total of 1170 tickets. Also, they have sold 80 more adult tickets than children's tickets. How
Many children's tickets have they sold?

A) 549
B) 545
C) 547
D) 541

Question 55

Use a graph to determine the number of solutions the system has.

Question 56

Solve the system graphically.

Question 57

Solve the problem.
A theatre sells two types of tickets to their plays; children's tickets and adult tickets. For today's performance they have sold a total of 900 tickets. Also, they have sold 4 times as many children's tickets as adult tickets. How
Many children's tickets have they sold?

A) 720
B) 53
C) 716
D) 727

Question 58

Solve the system graphically.

Question 59

Solve the problem.
A theatre sells two types of tickets to their plays; children's tickets and adult tickets. For today's performance they have sold a total of 1134 tickets. Also, they have sold 80 more adult tickets than children's tickets. How
Many adult tickets have they sold?

A) 592
B) 607
C) 605
D) 612

Question 60

Solve the system graphically.

- $$\begin{array} { l } x ^ { 2 } - y ^ { 2 } = 7.82 \\x = 2 y - 5 \\\begin{aligned}\text { </strong><div>A) } \approx ( - 2.97 , - 1.01 ) \text { and } \approx ( 6.31 , - 5.65 ) & \text {B) } \approx ( - 6.31,5.65 ) \text { and } \approx ( 2.97,1.01 ) \\\text { C) } \approx ( - 6.31 , - 5.65 ) \text { and } \approx ( 2.97 , - 1.01 ) & \text { D) } \approx ( - 2.97,1.01 ) \text { and } \approx ( 6.31,5.65 )\end{aligned}\end{array}$$

Question 61

Solve the problem.
The total number of cars sold at a used car lot for the years 1996 and 1997 was 1308. From 1996 to 1997 the number of cars sold declined by 158. How many cars were sold in 1997?

A) 575
B) 585
C) 581
D) 569

Question 62

Write the word or phrase that best completes each statement or answers the question.
Answer the question.
2x - 7y = -17
5x + 3y = 19
If your friend was going to solve this system of equations by first eliminating y, what general suggestions
would you make so your friend could start on this in a systematic way?

Question 63

Choose the one alternative that best completes the statement or answers the question.
Determine the order of the matrix.

Question 64

Solve the problem.
Find the equilibrium point for the given demand and supply curve. p = 4830 - 90x (demand)
P = 120x (supply)

A) (23, 2760)
B) (40, 1230)
C) (30, 2760)
D) (30, 2130)

Question 65

Solve the problem.
In one study the maximum heart rates of conditioned athletes were examined. A group of athletes was exercised to exhaustion. Let x represent an athlete's heart rate five seconds after stopping exercise and y represent an athlete's heart
Rate ten seconds after stopping exercise. It was found that the maximum heart rate H for these athletes satisfied the
Following two equations.
H = 0.491 x + 0.468 y + 11.2
H = -0.981 x + 1.872y + 26.4
If an athlete had a maximum heart rate of H = 160, determine the value of x graphically to the tenths place.

A) x = 157.3
B) x = 157.0
C) x = 156.2
D) x = 156.7

Question 66

Write the word or phrase that best completes each statement or answers the question.
Answer the question.
If the graphs of a system of two equations are a circle and a parabola, what are the possible numbers of
solutions (with real coordinates) of this system?

Question 67

Write the word or phrase that best completes each statement or answers the question.
Answer the question.
If the graphs of a system of two equations are a line and a parabola, what are the possible numbers of solutions
(with real coordinates) of this system?

Question 68

Solve.
Find the dimensions of a rectangular enclosure with perimeter 40 yd and area 91 yd2.

A) 15 yd by 6 yd
B) 13 yd by 7 yd
C) 14 yd by 6 yd
D) 16 yd by 7 yd

Question 69

Write the word or phrase that best completes each statement or answers the question.
Answer the question.
5x + 3y = 19
7x + 8y = 48
If your friend was going to solve this system of equations by first eliminating y, what general suggestions
would you make so your friend could start on this in a systematic way?

Question 70

Solve.
A rectangular plot has area 126 yd2 with a perimeter of 46 yd. What is the length of the longest side?

A) 13 yd
B) 14 yd
C) 16 yd
D) 12 yd

Question 71

Solve the problem.
Find the equilibrium point for the given demand and supply curve. p = 524 - 3x (demand)
P = 3x - 412 (supply)

A) (-412, 524)
B) (56, 156)
C) (521, 415)
D) (156, 56)

Question 72

Write the word or phrase that best completes each statement or answers the question.
Answer the question.
Consider the equation 5(-3 - x) + x = 14x - 5(3 - x). Now consider the following system of equations solvable by the
substitution method:
y = 5(-3 - x) + x
y = 14x - 5(3 - x).
Explain the connections that exist between the single equation and the system of two equations.

Question 73

Write the word or phrase that best completes each statement or answers the question.
Answer the question.
When using the substitution or elimination method to solve a system of two equations, you end up with an
equation stating 0 = 7. What does this indicate to you about the system of equations?

Question 74

Solve.
Find the dimensions of a rectangular garden with perimeter 62 yd and area 220 yd2.

A) 10 yd by 11 yd
B) 20 yd by 11 yd
C) 10 yd by 22 yd
D) 20 yd by 22 yd

Question 75

Write the word or phrase that best completes each statement or answers the question.
Answer the question.

Question 76

Write the word or phrase that best completes each statement or answers the question.
Answer the question.
If the graphs of a system of two equations are both circles, what are the possible numbers of solutions (with real
coordinates) of this system?

Question 77

Solve.
Find the dimensions of a rectangular enclosure with perimeter 34 ft and area 60 ft2.

A) 10 ft by 6 ft
B) 12 ft by 5 ft
C) 10 ft by 24 ft
D) 12 ft by 22 ft

Question 78

Write the word or phrase that best completes each statement or answers the question.
Answer the question.
When using the substitution or elimination method to solve a system of two equations, you end up with an
equation stating 0 = 0. What does this indicate to you about the system of equations?

Question 79

Write the word or phrase that best completes each statement or answers the question.
Answer the question.
If the graphs of a system of two equations are both parabolas, what are the possible numbers of solutions (with
real coordinates) of this system?

Question 80

Solve the problem.
The total number of cars sold at a used car lot for the years 1996 and 1997 was 592. The number of cars sold in 1997 was 3 times the number of cars sold in 1996. How many cars were sold in 1997?

A) 444
B) 147
C) 156
D) 448