Answer
$(4, -9)$
Work Step by Step
Add the equations together:
\begin{array}\\
6x+2y=6\\
\underline{-6x-5y=21}\\
0x-3y=27\\\\
\end{array}
Solve for $y$ to obtain:
\begin{align*}
-3y&=27\\
y&=\frac{27}{-3}\\
y&=-9\end{align*}
Substitute $-9$ to $y$ in the first equation to obtain:
\begin{align*}
6x+2y&=6\\
6x+2(-9)&=6\\
6x-18&=6\\
6x&=6+18\\
6x&=24
x&=\frac{24}{6}\\
x&=4
\end{align*}
Check by substituting $4$ to $x$ and $-9$ to $y$ in the second equation to obtain:
\begin{align*}
-6(4)-5(-9)&=21\\
-24+45&=21\\
21&\stackrel{\checkmark}=21
\end{align*}
Therefore, the solution is $(4, -9)$.
