Question

Solve for the z coordinate of the system
x+2y+5z=-1
2x-y+z=2
3x+4y-4z=14

Answer 1

x + 2y + 5z = -1 -->(-2)
2x - y + z = 2
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-2x - 4y - 10z = 2 (result of multiplying by -2)
2x - y + z = 2
------------------add
-5y - 9z = 4

2x - y + z = 2 ---->(3)
3x + 4y - 4z = 14 -->(-2)
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6x - 3y + 3z = 6 (result of multiplying by 3)
-6x - 8y + 8z = -28 (result of multiplying by -2)
-----------------add
-11y + 11z = - 22

-5y - 9z = 4 --->(-11)
-11y + 11z = -22 -->(5)
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55y + 99z = -44 (result of multiplying by -11)
-55y + 55z = - 110 (result of multiplying by 5)
------------------add
154z = - 154
z = -1

-5y - 9z = 4
-5y - 9(-1) = 4
-5y + 9 = 4
-5y = 4 - 9
-5y = -5
y = 1

x + 2y + 5z = -1
x + 2(1) + 5(-1) = -1
x + 2 - 5 = -1
x - 3 = -1
x = -1 + 3
x = 2

check...
2x - y + z = 2
2(2) - 1 - 1 = 2
4 - 2 = 2
2 = 2 (correct)

x = 2, y = 1, and z = -1