Label the equations A, B, C.
2A+B: 18x-z=-40. So x=(z-40)/18.
B-2C: 8y-7z=-52. So y=(7z-52)/8.
We have x and y in terms of z so we can substitute for x and y in any equation, so we choose A:
8(z-40)/18-(7z-52)/8+z=-9; (4z-160)/9-(7z-52)/8+z=-9;
Multiply through by 8*9=72:
8(4z-160)-9(7z-52)+72z=-648; 32z-1280-63z+468+72z=-648.
41z=164, so z=4. Therefore x=-36/18=-2 and y=-24/8=-3.
Check out solution in all original equations:
-16+3+4=-9; -4-6-12=-22; -2+9+8=15. Solution is (-2,-3,4).
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