Why do simultaneous equations sometimes work and sometimes not work???

[rose coyote]

I dont understand how this machine works

Oh I get it now

So the input is 3, multiplied by x minus y gives 5

And 7x-y = 25

7x - y = 25
And y = -5+3x

So 7x -(-5+3x) = 25
And 7x+5-3x = 25

You made a sign mistake

A subjectively better way for this case would be to write

y = 3x-5
y = 7x-25

Which implies
3x-5 = 7x-25

This is a good idea to have when one of the unknown coefficients is 1

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