$x-2y+2z=1$
$-2x+y-z=2$
$x-y+z=5$
I know the answer is no solution. If you eliminate x, you get the standard 0 equals a number. However, if you eliminate y or z as the first 2 steps, you get x equals different values. Why?
2026-04-06 22:16:06.1775513766
No solution system of three equations, but bogus answers when eliminating y or z first.
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The fact that you are getting more than one value for a variable means that the system is inconsistent and there is no defined solution.
In 3D, these equations define planes. In this case, the planes would not be intersecting at a fixed point. Instead they would be giving two or three lines. The 'bogus' values you get would be points on these lines.