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Note that x2−y2=(x−y)(x+y) ${x}^{2}-{y}^{2}=(x-y)(x+y)$. Hence,

{x2−y2x−y=55=11

can be rewritten in the form

{x+yx−y=5=11

Adding the two equations, we obtain2x=16 $2x=16$, and we conclude that x=8 $x=8$. Subtracting the two equations, we obtain 2y=−6 $2y=-6$, and we conclude that y=−3 $y=-3$.

can be rewritten in the form

Adding the two equations, we obtain

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