Answer
The solution set is $\left\{(0, 2)\right\}$.
Work Step by Step
Solve for $x$ in the second equation to obtain $x=2-y$.
Since $x=2-y$, substitute $2-y$ to $x$ in the first equation to obtain:
$3y=5(2-y)+6 \\ \implies 3y =10-5y+6
\\ \implies 8y=16 \\ \implies y=2$
Plug $y=2$ into $x+y=2$ to obtain:
$x+2=2 \\ \implies x=0$
So, the solution set is $\left\{(0, 2)\right\}$.
