[tex] \bf \begin{cases}
x^2-y^2=15\\
x+y=1\implies \boxed{y}=1-x
\end{cases}
\\\\\\
x^2-y^2=15\implies x^2-\left( \boxed{1-x} \right)^2=15\implies x^2-(\stackrel{FOIL}{1-2x+x^2})=15
\\\\\\
x^2-1+2x-x^2=15\implies 2x-1=15\implies 2x=16
\\\\\\
x=\cfrac{16}{2}\implies x=8
\\\\\\
\stackrel{\textit{substituting \underline{x} in the second equation}}{(8)+y=1}\implies y=-7\\\\
-------------------------------\\\\
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(8, -7) [/tex]
