If $ax + by = a^2 - b^2$ and $bx + ay = 0$, then the value of $x + y$ is :

Question

Accepted Answer

## Model Answer **Option C: $a - b$** Adding both equations: $(a+b)x + (a+b)y = a^2 - b^2$, so $(a+b)(x+y) = (a+b)(a-b)$, giving $x + y = a - b$. ## Explanation Add the two equations directly: $(a+b)x + (a+b)y = a^2 - b^2$. Factor both sides: $(a+b)(x+y) = (a+b)(a-b)$. Divide by $(a+b)$ (assuming $a 
eq -b$) to get $x+y = a-b$. This elimination shortcut finds $x+y$ without solving for $x$ and $y$ individually — a common MCQ technique examiners expect you to recognise.

Mathematics — CBSE Class 10 board question