SOLVING SYSTEMS OF EQUATIONS CRAMER RULE WORKSHEET

Using Cramer's rule solve the system of equations.

Problem 1 :

-x + y = -5

-5x - 2y + 6z = -5

-4x - y + 2z = 8

Solution

Problem 2 :

-4x - 2y - z = -11

-x - 2y = -6

x - y - 5z = 5

Solution

Problem 3 :

5x + 2y + 2z = 9

-6x - 4y - 3z = -19

x - 2y = -9

Solution

Problem 4 :

4a + 4c = 4

4a - 3b + c = -14

-2a - 3b - 5c = -20

Solution

Problem 5 :

4x - 4y + 2z = -14

4x + 2y = 14

-3y + z = -10

Solution

Answer Key

1)  So, the values of x, y and z are -3, -8 and -6 respectively.

2)  So, the values of x, y and z are 2, 2 and -1 respectively.

3)  So, the values of x, y and z are -1, 4 and 3 respectively.

4)  System is consistent and it has infinitely many solution.

5)  System is inconsistent and it has no solution

Use Cramer's Rule to solve each system.

Problem 1 :

x - 5y = -5

-4x - 2y = 20

Solution

Problem 2 :

-x + 5y = 2

x - 2y = -2

Solution

Problem 3 :

2x + 2y = 0

4x - y = -20

Solution

Problem 4 :

3x - 4y = 1

-5x + 2y = 3

Solution

Problem 5 :

-x - y = -1

3x + 3y = 3

Solution

Problem 6 :

-5x + 5y = 10

-2x + 2y = -4

Solution

Answer Key

1)  Solution is (-5, 0).

2)  Solution is (-2, 0).

3)  Solution is (-4, 4).

4)  Solution is (-1, 1).

5)  The system is consistent and it has infinitely many solution.

6)  So, the system is inconsistent and it has no solution.

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