Systems of Three Equations Substitution - Kuta Software

Kuta Software - Infinite Algebra 2

Name___________________________________

Solving Systems of Three Equations w/ Substitution Date________________ Period____

Solve each system by substitution.

1) -x - y - 3z = -9 z = -3x - 1 x = 5 y - z + 23

2) x = -4z - 19 y = 5x + z - 4 -5 y - z = 25

3) y = x + z + 5 z = -3 y - 3 2x - y = -4

4) -2 y + 5z = -3 y = -5x - 4z - 5 x = 4z + 4

5) y = x + 4z - 5 4x + 3y - 2z = 5 z = -2x + 2

6) x = 3 y - 3z + 8 z = 4x + 5y - 14 3 y + 2z = 14

7) -5x - 3 y + z = -4 -2x - 2y + 2z = 4 z = x + 5

8) -4x + 2z = 14 y = x + z + 12 -2x - 4z = 22

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Worksheet by Kuta Software LLC

9) 3x - 3 y = -6 z = -3x - 3y + 9 -4x + 5y + z = 8

10) x = -5 y + 4z + 1 x - 2 y + 3z = 1 2x + 3y - z = 2

11) a - 2b + c = -6 a + 5c = -12 -a + 6b + 4c = 3

12) -2x + 3 y + 5z = -21 -4z = 20 6x - 3y = 0

13) 2x - 4z = 20 -3x + y - 4z = 20 -4x + 2 y + 3z = -15

14) x + 3 y = -17 3x = -6 4x - 3 y + 6z = 25

15) 5r + 4s - 6t = -24 -2s + 2t = 0 s - t = 2

16) -5r + 5s + 3t = -23 -5r + 3s - 3t = -11 -6r + 6t = -12

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 2

Name___________________________________

Solving Systems of Three Equations w/ Substitution Date________________ Period____

Solve each system by substitution.

1) -x - y - 3z = -9 z = -3x - 1 x = 5 y - z + 23

(-2, -4, 5)

2) x = -4z - 19 y = 5x + z - 4 -5 y - z = 25

(1, -4, -5)

3) y = x + z + 5 z = -3 y - 3 2x - y = -4

(-2, 0, -3)

4) -2 y + 5z = -3 y = -5x - 4z - 5 x = 4z + 4

(0, -1, -1)

5) y = x + 4z - 5 4x + 3y - 2z = 5 z = -2x + 2

(0, 3, 2)

6) x = 3 y - 3z + 8 z = 4x + 5y - 14 3 y + 2z = 14

(2, 2, 4)

7) -5x - 3 y + z = -4 -2x - 2y + 2z = 4 z = x + 5

(0, 3, 5)

8) -4x + 2z = 14 y = x + z + 12 -2x - 4z = 22

(-5, 4, -3)

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Worksheet by Kuta Software LLC

9) 3x - 3 y = -6 z = -3x - 3y + 9 -4x + 5y + z = 8

(1, 3, -3)

10) x = -5 y + 4z + 1 x - 2 y + 3z = 1 2x + 3y - z = 2

No unique solution

11) a - 2b + c = -6 a + 5c = -12 -a + 6b + 4c = 3

(3, 3, -3)

13) 2x - 4z = 20 -3x + y - 4z = 20 -4x + 2 y + 3z = -15

(0, 0, -5)

12) -2x + 3 y + 5z = -21 -4z = 20 6x - 3y = 0

(1, 2, -5)

14) x + 3 y = -17 3x = -6 4x - 3 y + 6z = 25

(-2, -5, 3)

15) 5r + 4s - 6t = -24 -2s + 2t = 0 s - t = 2

No unique solution

16) -5r + 5s + 3t = -23 -5r + 3s - 3t = -11 -6r + 6t = -12

(1, -3, -1)

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Worksheet by Kuta Software LLC

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