, 2025

Solution 1:

Factoring the left side of the equation $x^2-y^2=72$ gives $(x-y)(x+y)=72$.

Substituting $x-y=12$ into this
equation, we get $12(x+y)=72$, and so
$x+y=\dfrac{72}{12}=6$.

Solution 2:

Solving the system of equations, we substitute the second equation
$x=12+y$ into the first equation
$x^2-y^2=72$ to get $(12+y)^2-y^2=72$.

Solving, we have $144+24y+y^2-y^2=72$
or $24y=-72$, and so $y=\dfrac{-72}{24}=-3$.

Since $x=12+y=12-3=9$, then $x+y=9-3=6$.