7.05 Systems of Equations and Inequalities Unit Exam

Question 13

Solve by the substitution method.4x + 3y = 13
x + y = 4

Question 14

Solve by the elimination method.2x + 3y = 18
5x – y = 11

Question 15

Solve by the elimination methods.9x + 2y = 2
21x + 6y = 4

Question 16

1. Solve using matrices.7x + 5y = 14
   4x + 3y = 9
   

   		(7, -3)
   		(-3, 7)
   		(3, -7)
   		(7, 3)

2 points

Question 17

1. Solve using matrices.x – 5y = -5
   -4x – 2y = 20
   

   		No solution
   		(-5, 0)
   		(0, 1)
   		(5, -2)

2 points

Question 18

1. One number is 7 more than another number. The sum of the numbers is 63. What are the numbers?
   

   		10 and 7
   		30 and 37
   		28 and 35
   		54 and 9

2 points

Question 19

1. Which of the following is NOT a solution to the system of inequalities?
   
   

   		(2, 3)
   		(1, 3)
   		(0, 3)
   		(0, 4)

2 points

Question 20

1. What is the system of inequalities associated with the following graph?
   
   

   		x + y > 2 2x – y > 1
   		x + y < 2 2x – y < 1
   		x + y > 2 2x – y < 1
   		x + y < 2 2x – y > 1

2 points

Question 21

1. Solve using matrices.3x – 2y + z = -5
   -2x + 3y – 3z = 12
   3x – 2y – 2z = 4
   

   		(1, 0, -3)
   		(1, -3, 0)
   		(0, 1, -3)
   		(0, -3, 1)

2 points

Question 22

1. Solve using matrices.3x – y = -1
   2x – y + z = -6
   x + 4y – z = 9
   

   		(0, 1, -5)
   		(2, 7, -3)
   		(1, 4, -4)
   		(0, 1, 5)

2 points

Question 23

1. The
   largest angle in a triangle is equal to the sum of the two other
   angles. The middle angle is twice the measure of the smallest angle.
   What is the measure of each angle?
   

   		32°, 64°, 90°
   		30°, 60°, 80°
   		30°, 60°, 90°
   		30°, 60°, 100°

2 points

Question 24

1. Evaluate
   

Question 25

Evaluate

Question 26

1. If matrix A has dimensions 4 x 1 and matrix B has dimensions 1 x 5, can matrix A and matrix B be multiplied?
   

   		yes
   		no

2 points

Question 27

1. If matrix A has dimensions 2 x 5 and matrix B has dimensions 5 x 5, can matrix A and matrix B be multiplied?
   

   		yes
   		no

2 points

Question 28

1. Evaluate
   

Question 29

Evaluate

Question 30

Find the determinant of

Question 31

Find the determinant of

Question 32

Solve using the substitution method.x – 2y = 5
2x – 4y = 1

Question 33

Solve by the substitution method.y – 3x = 5
y + x = 3

Question 34

Solve using the elimination method.x – 3y = -17
-x + 8y = 52

Question 35

Solve using the elimination method.3x + 2y = 7
5x – 2y = 1

Question 36

Solve using matrices.4x + 5y = 40
x – y = 1

Question 37

Solve using matrices.3x + 5y = -4
x + 2y = -2

Question 38

Find the value of two numbers if their sum is 12 and their difference is 4.

Question 39

1. What is the system of inequalities associated with the following graph?
   
   

   		3x + y ? -3 x + 2y ? 4
   		-3x – y ? -3 x + 2y ? 4
   		3x + y ? -3 x – 2y ? 4
   		3x – y ? 3 x – 2y ? 4

2 points

Question 40

1. What is the system of inequalities associated with the following graph?
   
   

   		–x – y ? -3 x + y ? 3
   		x + y ? -3 x + y ?3
   		x + y ? -3 x + y ? 3
   		x + y ? -3 x – y ? 3

2 points

Question 41

1. Solve using matrices.x – 3y + z = -9
   x + y – 3z = -5
   3x – y + z = 11

Question 42