Solve the following system if equations for all three variables

Question

9x+4y+9z=3

-9x-2y-7z=1

-x+2y+z=5

Answer 1

eliminates x

Equation 1 + Equation 2

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2y + 2z = 4

y + z = 2

z = 2 - y

9 * Equation 3 + equation 1

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22y + 18z = 48

11y + 9z = 24

11y + 9 (2 - y) = 24

11y + 18 - 9y = 24

2y + 18 = 24

2y = 6

y = 3

z = 2 - 3 = -1

9x + 4(3) + 9 (-1) = 3

9x + 12 - 9 = 3

9x + 3 = 3

9x = 0

x = 0

(x=0, y=3, z=-1)