This looks like a lot of
"Much Ado About Nothing"
If your equations are
x+y = 6 , why not just add them as they are?
x=9/5 or 1.8
sub into x+y=6
you can get
y = 4.2
your solution of x=6, y=3 work in your second equation, but not in the first.
So your solution is incorrect.
The error was when you added your equations
-5y = -21
y = -21/-5 = 4.2
solve one equation for x and plug the answer to the other equation and solve it
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