Systems of Three Equations Elimination - Kuta Software
Kuta Software - Infinite Algebra 2
Name___________________________________
Solving Systems of Three Equations w/ Elimination Date________________ Period____
Solve each system by elimination.
1) -x - 5 y - 5z = 2 4x - 5 y + 4z = 19 x + 5 y - z = -20
2) -4x - 5y - z = 18 -2x - 5 y - 2z = 12 -2x + 5 y + 2z = 4
3) -x - 5 y + z = 17 -5x - 5y + 5z = 5 2x + 5 y - 3z = -10
4) 4x + 4y + z = 24 2x - 4y + z = 0 5x - 4 y - 5z = 12
5) 4r - 4s + 4t = -4 4r + s - 2t = 5 -3r - 3s - 4t = -16
6) x - 6 y + 4z = -12 x + y - 4z = 12 2x + 2 y + 5z = -15
7) x - y - 2z = -6 3x + 2 y = -25 -4x + y - z = 12
8) 5a + 5b + 5c = -20 4a + 3b + 3c = -6 -4a + 3b + 3c = 9
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Worksheet by Kuta Software LLC
9) -6r + 5s + 2t = -11 -2r + s + 4t = -9 4r - 5s + 5t = -4
11) 5x - 4 y + 2z = 21 -x - 5 y + 6z = -24 -x - 4 y + 5z = -21
10) -6x - 2 y + 2z = -8 3x - 2 y - 4z = 8 6x - 2 y - 6z = -18
12) 6r - s + 3t = -9 5r + 5s - 5t = 20 3r - s + 4t = -5
13) -3a - b - 3c = -8 -5a + 3b + 6c = -4 -6a - 4b + c = -20
14) -5x + 3 y + 6z = 4 -3x + y + 5z = -5 -4x + 2y + z = 13
15) 3a - 3b + 4c = -23 a + 2b - 3c = 25 4a - b + c = 25
16) -6x - 2y - z = -17 5x + y - 6z = 19 -4x - 6 y - 6z = -20
Critical thinking question:
17) Write a system of equations with the
solution (2, 1, 0).
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Solving Systems of Three Equations w/ Elimination Date________________ Period____
Solve each system by elimination.
1) -x - 5 y - 5z = 2 4x - 5 y + 4z = 19 x + 5 y - z = -20
(-2, -3, 3)
2) -4x - 5y - z = 18 -2x - 5 y - 2z = 12 -2x + 5 y + 2z = 4
(-4, 0, -2)
3) -x - 5 y + z = 17 -5x - 5y + 5z = 5 2x + 5 y - 3z = -10
(-1, -4, -4)
4) 4x + 4y + z = 24 2x - 4y + z = 0 5x - 4 y - 5z = 12
(4, 2, 0)
5) 4r - 4s + 4t = -4 4r + s - 2t = 5 -3r - 3s - 4t = -16
(1, 3, 1)
6) x - 6 y + 4z = -12 x + y - 4z = 12 2x + 2 y + 5z = -15
(0, 0, -3)
7) x - y - 2z = -6 3x + 2 y = -25 -4x + y - z = 12
(-5, -5, 3)
8) 5a + 5b + 5c = -20 4a + 3b + 3c = -6 -4a + 3b + 3c = 9
No unique solution
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Worksheet by Kuta Software LLC
9) -6r + 5s + 2t = -11 -2r + s + 4t = -9 4r - 5s + 5t = -4
(4, 3, -1)
11) 5x - 4 y + 2z = 21 -x - 5 y + 6z = -24 -x - 4 y + 5z = -21
(5, -1, -4)
10) -6x - 2 y + 2z = -8 3x - 2 y - 4z = 8 6x - 2 y - 6z = -18 No unique solution
12) 6r - s + 3t = -9 5r + 5s - 5t = 20 3r - s + 4t = -5
(-1, 6, 1)
13) -3a - b - 3c = -8 -5a + 3b + 6c = -4 -6a - 4b + c = -20
(2, 2, 0)
14) -5x + 3 y + 6z = 4 -3x + y + 5z = -5 -4x + 2y + z = 13
(-2, 4, -3)
15) 3a - 3b + 4c = -23 a + 2b - 3c = 25 4a - b + c = 25
No unique solution
16) -6x - 2y - z = -17 5x + y - 6z = 19 -4x - 6 y - 6z = -20
(2, 3, -1)
Critical thinking question:
17) Write a system of equations with the
solution (2, 1, 0).
Many answers. Ex: x + y + z = 3, 2x + y + z = 5, x + 2 y - z = 4
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at
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Worksheet by Kuta Software LLC
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