Solving Systems with Matrices

Question 1

For the system x - y = -3 and 3x + y = 7, what is the coefficient matrix?

Accepted Answer

1 -1 3 1

Answer

1 3 -1 1

Answer

-3 7

Answer

1 -1 -3 3 1 7

Question 2

The system is x - 5y = -13 and 5x + y = 13. Which matrix equation represents it?

Accepted Answer

1 -5 5 1 * x y = -13 13

Answer

1 5 -5 1 * x y = -13 13

Answer

-13 13 * x y = 1 -5 5 1

Answer

1 -5 5 1 * -13 13 = x y

Question 3

The system is 3x + 3y = 12 and x - y = -6. Which matrix equation represents it?

Accepted Answer

3 3 1 -1 * x y = 12 -6

Answer

3 1 3 -1 * x y = 12 -6

Answer

12 -6 * x y = 3 3 1 -1

Answer

3 3 1 -1 * 12 -6 = x y

Question 4

For the system 4x - y = 7 and 2x - 4y = 4, the coefficient matrix has determinant -14. What does that tell you?

Accepted Answer

the system has exactly one solution, which multiplying the inverse by the constants finds

Answer

the system has infinitely many solutions, so the inverse method cannot be used

Answer

the system has no solution, so the inverse method cannot be used

Answer

the coefficient matrix must have been written incorrectly

Question 5

The system is 2x - 2y = 10 and 5x + 2y = 11. Which matrix equation represents it?

Accepted Answer

2 -2 5 2 * x y = 10 11

Answer

2 5 -2 2 * x y = 10 11

Answer

10 11 * x y = 2 -2 5 2

Answer

2 -2 5 2 * 10 11 = x y

Question 6

For the system x + 5y = 8 and 3x - 3y = -1, what is the constant matrix?

Accepted Answer

8 -1

Answer

1 5 3 -3

Answer

1 3

Question 7

The system is 5x - 3y = 1 and x + 5y = 17. Which matrix equation represents it?

Accepted Answer

5 -3 1 5 * x y = 1 17

Answer

5 1 -3 5 * x y = 1 17

Answer

1 17 * x y = 5 -3 1 5

Answer

5 -3 1 5 * 1 17 = x y

Question 8

For the system x - 3y = 12 and 4x + y = 5, what is the constant matrix?

Accepted Answer

12 5

Answer

1 -3 4 1

Answer

1 4

Question 9

The system is x - 4y = 11 and 5x + 3y = 9. Which matrix equation represents it?

Accepted Answer

1 -4 5 3 * x y = 11 9

Answer

1 5 -4 3 * x y = 11 9

Answer

11 9 * x y = 1 -4 5 3

Answer

1 -4 5 3 * 11 9 = x y

Question 10

The system is 4x + y = 11 and x + 3y = 11. Which matrix equation represents it?

Accepted Answer

4 1 1 3 * x y = 11 11

Answer

11 11 * x y = 4 1 1 3

Answer

4 1 1 3 * 11 11 = x y

Answer

1 4 3 1 * x y = 11 11

Question 11

Solve the system 2x + 2y = 16 and 4x + y = 17 by writing it as AX = B and computing A^-1 B. What is the solution?

Accepted Answer

(3, 5)

Answer

(5, 3)

Answer

(-3, 5)

Answer

(3, -5)

Question 12

The system is 5x - 3y = 17 and 3x - 4y = 8. Which matrix equation represents it?

Accepted Answer

5 -3 3 -4 * x y = 17 8

Answer

5 3 -3 -4 * x y = 17 8

Answer

17 8 * x y = 5 -3 3 -4

Answer

5 -3 3 -4 * 17 8 = x y

Question 13

Solve the system 5x - y = 18 and 2x + 5y = 18 by writing it as AX = B and computing A^-1 B. What is the solution?

Accepted Answer

(4, 2)

Answer

(2, 4)

Answer

(-4, 2)

Answer

(4, -2)

Question 14

Solve the system 3x + 5y = 13 and 5x - 5y = 35 by writing it as AX = B and computing A^-1 B. What is the solution?

Accepted Answer

(6, -1)

Answer

(-1, 6)

Answer

(-6, -1)

Answer

(6, 1)

Question 15

For the system 4x + 5y = 7 and 3x - 4y = 4, the coefficient matrix has determinant -31. What does that tell you?

Accepted Answer

the system has exactly one solution, which multiplying the inverse by the constants finds

Answer

the system has infinitely many solutions, so the inverse method cannot be used

Answer

the system has no solution, so the inverse method cannot be used

Answer

the coefficient matrix must have been written incorrectly

Question 16

For the system x - 4y = 7 and 4x + y = 4, the coefficient matrix has determinant 17. What does that tell you?

Accepted Answer

the system has exactly one solution, which multiplying the inverse by the constants finds

Answer

the system has infinitely many solutions, so the inverse method cannot be used

Answer

the system has no solution, so the inverse method cannot be used

Answer

the coefficient matrix must have been written incorrectly

Question 17

The system is x - 2y = -11 and 4x + y = 1. Which matrix equation represents it?

Accepted Answer

1 -2 4 1 * x y = -11 1

Answer

1 4 -2 1 * x y = -11 1

Answer

-11 1 * x y = 1 -2 4 1

Answer

1 -2 4 1 * -11 1 = x y

Question 18

Solve the system 2x + 3y = 16 and 5x - 3y = -2 by writing it as AX = B and computing A^-1 B. What is the solution?

Accepted Answer

(2, 4)

Answer

(4, 2)

Answer

(-2, 4)

Answer

(2, -4)

Question 19

A cart sells 5 tacos and 1 soda for $14.00, and 2 tacos and 6 sodas for $28.00. Writing this as AX = B with x the price of one taco and y the price of one soda, what is the price of one taco?

Accepted Answer

$2.00

Answer

$4.00

Answer

$2.50

Answer

$1.50

Question 20

Solve the system x + 4y = 9 and 3x + 2y = 17 by writing it as AX = B and computing A^-1 B. What is the solution?

Accepted Answer

(5, 1)

Answer

(1, 5)

Answer

(-5, 1)

Answer

(5, -1)

Question 21

Solve the system 3x + y = -3 and 4x - y = -11 by writing it as AX = B and computing A^-1 B. What is the solution?

Accepted Answer

(-2, 3)

Answer

(3, -2)

Answer

(2, 3)

Answer

(-2, -3)

Question 22

The system is x + 5y = -7 and 5x + y = 13. Which matrix equation represents it?

Accepted Answer

1 5 5 1 * x y = -7 13

Answer

-7 13 * x y = 1 5 5 1

Answer

1 5 5 1 * -7 13 = x y

Answer

1 5 5 1 * x y = 13 -7

Question 23

Solve the system 5x - 4y = 21 and 2x - 4y = 6 by writing it as AX = B and computing A^-1 B. What is the solution?

Accepted Answer

(5, 1)

Answer

(1, 5)

Answer

(-5, 1)

Answer

(5, -1)

Question 24

For the system 5x + y = 12 and 3x - 5y = 5, what is the constant matrix?

Accepted Answer

12 5

Answer

5 1 3 -5

Answer

5 3

Question 25

For the system 3x + 2y = 12 and 4x - 5y = 5, what is the coefficient matrix?

Accepted Answer

3 2 4 -5

Answer

3 4 2 -5

Answer

12 5

Answer

3 2 12 4 -5 5

Question 26

The system is 3x - 5y = -28 and x - 5y = -26. Which matrix equation represents it?

Accepted Answer

3 -5 1 -5 * x y = -28 -26

Answer

3 1 -5 -5 * x y = -28 -26

Answer

-28 -26 * x y = 3 -5 1 -5

Answer

3 -5 1 -5 * -28 -26 = x y

Question 27

Solve the system 2x + 3y = 16 and 4x + y = 12 by writing it as AX = B and computing A^-1 B. What is the solution?

Accepted Answer

(2, 4)

Answer

(4, 2)

Answer

(-2, 4)

Answer

(2, -4)

Question 28

For the system 2x - 4y = 9 and 4x + 3y = -2, the coefficient matrix has determinant 22. What does that tell you?

Accepted Answer

the system has exactly one solution, which multiplying the inverse by the constants finds

Answer

the system has infinitely many solutions, so the inverse method cannot be used

Answer

the system has no solution, so the inverse method cannot be used

Answer

the coefficient matrix must have been written incorrectly

Question 29

For the system 3x - y = 6 and 5x - 2y = 6, what is the coefficient matrix?

Accepted Answer

3 -1 5 -2

Answer

3 5 -1 -2

Answer

6 6

Answer

3 -1 6 5 -2 6

Question 30

For the system 2x - 5y = -3 and 5x - 2y = 7, what is the constant matrix?

Accepted Answer

-3 7

Answer

2 -5 5 -2

Answer

2 5

Question 31

A cart sells 5 tacos and 1 soda for $11.50, and 2 tacos and 6 sodas for $27.00. Writing this as AX = B with x the price of one taco and y the price of one soda, what is the price of one taco?

Accepted Answer

$1.50

Answer

$4.00

Answer

$2.00

Answer

$1.00

Question 32

For the system 5x + 4y = 6 and 3x - 3y = 6, what is the constant matrix?

Accepted Answer

6 6

Answer

5 4 3 -3

Answer

5 3

Question 33

A stand sells 5 pretzels and 1 lemonade for $17.00, and 2 pretzels and 6 lemonades for $18.00. Writing this as AX = B with x the price of one pretzel and y the price of one lemonade, what is the price of one pretzel?

Accepted Answer

$3.00

Answer

$2.00

Answer

$3.50

Answer

$2.50

Question 34

Solve the system 4x - 4y = -20 and 3x - 4y = -21 by writing it as AX = B and computing A^-1 B. What is the solution?

Accepted Answer

(1, 6)

Answer

(6, 1)

Answer

(-1, 6)

Answer

(1, -6)

Question 35

For the system 4x + 5y = 9 and x - 5y = -2, the coefficient matrix has determinant -25. What does that tell you?

Accepted Answer

the system has exactly one solution, which multiplying the inverse by the constants finds

Answer

the system has infinitely many solutions, so the inverse method cannot be used

Answer

the system has no solution, so the inverse method cannot be used

Answer

the coefficient matrix must have been written incorrectly

Question 36

Solve the system 3x - 5y = -16 and x - 2y = -7 by writing it as AX = B and computing A^-1 B. What is the solution?

Accepted Answer

(3, 5)

Answer

(5, 3)

Answer

(-3, 5)

Answer

(3, -5)

Question 37

A stand sells 5 pretzels and 1 lemonade for $16.50, and 2 pretzels and 6 lemonades for $15.00. Writing this as AX = B with x the price of one pretzel and y the price of one lemonade, what is the price of one pretzel?

Accepted Answer

$3.00

Answer

$1.50

Answer

$3.50

Answer

$2.50

Question 38

Solve the system 3x + 4y = 27 and 2x + 2y = 14 by writing it as AX = B and computing A^-1 B. What is the solution?

Accepted Answer

(1, 6)

Answer

(6, 1)

Answer

(-1, 6)

Answer

(1, -6)

Question 39

For the system 3x - 3y = 7 and 5x + 2y = 4, the coefficient matrix has determinant 21. What does that tell you?

Accepted Answer

the system has exactly one solution, which multiplying the inverse by the constants finds

Answer

the system has infinitely many solutions, so the inverse method cannot be used

Answer

the system has no solution, so the inverse method cannot be used

Answer

the coefficient matrix must have been written incorrectly

Question 40

Solve the system 4x - 5y = -23 and 5x - 2y = -16 by writing it as AX = B and computing A^-1 B. What is the solution?

Accepted Answer

(-2, 3)

Answer

(3, -2)

Answer

(2, 3)

Answer

(-2, -3)

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Solving Systems with Matrices

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Solving Systems with Matrices

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner