CAT 2021 Slot 2 · Quant · Question 3

Do not solve for x and y separately.

Adding the two equations makes x-y appear on its own:

{x}^{2}-xy-x+{y}^{2}-xy+y=56,

that is \left({x}^{2}-2xy+{y}^{2}\right)-\left( x-y \right)=56, so {\left( x-y \right)}^{2}-\left( x-y \right)=56.

Writing d=x-y: {d}^{2}-d-56=0,

so \left( d-8 \right)\left( d+7 \right)=0 and d=8 or d=-7.

Since x>y, d is positive, so x-y=8.