Answer
$(x,y) =\left(2, 2\right) $
Work Step by Step
Give $$\begin{cases}
x&=4 y-6 \\
\frac{1}{2} x+6 y&=13.
\end{cases}$$ Write $x$ as a function of $y$ for the second function.
\begin{equation}
\begin{aligned}
x&=4 y-6\\
\left(\frac{1}{2} x+6 y\right)\cdot 2&=13\cdot 2\\
x+12y&= 26\\
x&= -12y+26.
\end{aligned}
\end{equation} Substitute the expression for the first equation into the second and solve for $y$.
\begin{equation}
\begin{aligned}
4y-6&=-12y+26\\
4y+12y&=26+6\\
16y &= 32\\
y&= \frac{32}{16}\\
&= 2.\\
x&=4\cdot (2)-6\\
& = 2.
\end{aligned}
\end{equation} The solution set is $(x,y) =\left(2, 2\right) $ Check
\begin{equation}
\begin{aligned}
2&\stackrel{?}{=}4 \cdot 2-6\\
2&= 2\ \checkmark\\
\end{aligned}
\end{equation}
