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x - 4y + 9 = 0

y - 3x + 5 = 0

If I set them equal to each other then I get no where because I'll have both x and y in the answer. But if I solve one of them for x or y then plug it into the other I can isolate one of them and then get an answer for x and y. Then by re-substitution I'll get answers for both x and y.

The only way setting them equal to each other would work is if x or y had values that cancelled during that time which in this case they don't. Is there a mathematical logic rule governing this? Or is it just by practice we know it has to be done this way? Thanks