prove or disprove 3x + 5y = 135 --> x is odd or y is odd:

Question

Can I prove this in words by: Suppose x is odd, then 3x + 5y will be odd and 135 ——> x is even. Left side doesn't equal to Right side. Hence y is odd.

Answer 1

Any integer multiplied by an even number is even. In addition, adding two integers of the same parity (even/odd) is even. Hence, if both $x$ and $y$ are even, then $3x+5y$ is even. This is a contradiction, as 135 is an odd number. Thus, either $x$ or $y$ is odd.