Answer
$\{ (-6,0), (0,6) \}$
Work Step by Step
Substituting $y=x+6$ into the first equation results to
\begin{array}{l}
x^2+(x+6)^2=36
\\\\
x^2+x^2+12x+36=36
\\\\
2x^2+12x=0
\\\\
x^2+6x=0
\\\\
x(x+6)=0
\\\\
x=\{-6,0\}
.\end{array}
Substituting $x=-6$ into the 2nd equation results to
\begin{array}{l}
y=-6+6\\\\
y=0
.\end{array}
Substituting $x=0$ into the 2nd equation results to
\begin{array}{l}
y=0+6\\\\
y=6
.\end{array}
Hence, the solution set is $
\{ (-6,0), (0,6) \}
$.
