Worksheet by Kuta Software LLC ... Solving Systems of Three Equations w/
Elimination ... 17) Write a system of equations with the solution (2, 1, 0). -2- ... (4,
2, 0). 5) 4r − 4s + 4t = −4. 4r + s − 2t = 5. −3r − 3s − 4t = −16. (1, 3, 1). 6) x − 6y +
4z = − ...
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 4 x − 5 y + 4z = 19 x + 5 y − z = −20
2) −4 x − 5 y − z = 18 −2 x − 5 y − 2z = 12 −2 x + 5 y + 2z = 4
3) − x − 5 y + z = 17 −5 x − 5 y + 5z = 5 2 x + 5 y − 3z = −10
4) 4 x + 4 y + z = 24 2x − 4 y + z = 0 5 x − 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 2 x + 2 y + 5z = −15
7) x − y − 2z = −6 3 x + 2 y = −25 −4 x + 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
10) −6 x − 2 y + 2z = −8 3 x − 2 y − 4z = 8 6 x − 2 y − 6z = −18
11) 5 x − 4 y + 2z = 21 − x − 5 y + 6z = −24 − x − 4 y + 5z = −21
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) −5 x + 3 y + 6z = 4 −3 x + y + 5z = −5 −4 x + 2 y + z = 13
15) 3a − 3b + 4c = −23 a + 2b − 3c = 25 4a − b + c = 25
16) −6 x − 2 y − z = −17 5 x + y − 6z = 19 −4 x − 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 4 x − 5 y + 4z = 19 x + 5 y − z = −20
2) −4 x − 5 y − z = 18 −2 x − 5 y − 2z = 12 −2 x + 5 y + 2z = 4
(−2, −3, 3)
3) − x − 5 y + z = 17 −5 x − 5 y + 5z = 5 2 x + 5 y − 3z = −10
(−4, 0, −2)
4) 4 x + 4 y + z = 24 2x − 4 y + z = 0 5 x − 4 y − 5z = 12
(−1, −4, −4)
5) 4r − 4s + 4t = −4 4r + s − 2t = 5 −3r − 3s − 4t = −16
(4, 2, 0)
6) x − 6 y + 4z = −12 x + y − 4z = 12 2 x + 2 y + 5z = −15
(1, 3, 1)
7) x − y − 2z = −6 3 x + 2 y = −25 −4 x + y − z = 12
(0, 0, −3)
8) 5a + 5b + 5c = −20 4a + 3b + 3c = −6 −4a + 3b + 3c = 9
(−5, −5, 3)
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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
10) −6 x − 2 y + 2z = −8 3 x − 2 y − 4z = 8 6 x − 2 y − 6z = −18
(4, 3, −1)
11) 5 x − 4 y + 2z = 21 − x − 5 y + 6z = −24 − x − 4 y + 5z = −21
No unique solution
12) 6r − s + 3t = −9 5r + 5s − 5t = 20 3r − s + 4t = −5
(5, −1, −4)
13) −3a − b − 3c = −8 −5a + 3b + 6c = −4 −6a − 4b + c = −20
(−1, 6, 1)
14) −5 x + 3 y + 6z = 4 −3 x + y + 5z = −5 −4 x + 2 y + z = 13
(2, 2, 0)
15) 3a − 3b + 4c = −23 a + 2b − 3c = 25 4a − b + c = 25
(−2, 4, −3)
16) −6 x − 2 y − z = −17 5 x + y − 6z = 19 −4 x − 6 y − 6z = −20
(2, 3, −1)
No unique solution
Critical thinking question: 17) Write a system of equations with the solution (2, 1, 0). Many answers. Ex: x + y + z = 3, 2 x + y + z = 5, x + 2 y − z = 4
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Worksheet by Kuta Software LLC
