Solve the system of linear equations

Question

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x − 2y + 3z = 7
4x + 5y + z = −1
−x + y − 2z = −4
What is the value of z, y, and x?

Answer 1

Add:
x-2y+3z = 7
-x+y-2z = -4
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-y+z = 3

Add #2 and 4*#3:
4x+5y+z = -1
-4x+4y-8z = -16
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9y-7z = -17

Now you know that z = y+3,so
9y-7(y+3) = -17
9y-7y-21 = -17
2y = 4
y = 2
so, z = 5, x = -4