Answer
$(5,-8)$
Work Step by Step
Alphabetical order: $a$ on the horizontal axis, $b$ on the vertical.
Graphing $b+2a=2$
Set $b=0 \Rightarrow a=1 \qquad $... $(1,0)$
Set $a=0 \Rightarrow b=2 \qquad $... $(0,2) $
Graphing $a=-3-b$
Set $b=0 \Rightarrow a=-3 \qquad $... $(-3,0)$
Set $a=0 \Rightarrow b=-3 \qquad $... $(0,-3)$
Graphically solving: $a=5,\ b=-8$.
Checking:$\qquad \left\{\begin{array}{lll}
-8+2(5) =2 & \Rightarrow & -8+10=2 \\
& & \\
5=-3-(-8) & \Rightarrow & 5=-3+8
\end{array}\right.$
both equations are satisfied, $(5,-8)$ is the solution.