Answer
$\left(3,\dfrac{1}{2}\right)$
Work Step by Step
Cancel the $x$-variable in the given system,
\begin{align*}
2x-6y&=3
\\
-3x+8y&=-5
\end{align*}
These result to the equivalent system,
\begin{align*}
6x-18y&=9
&(1)
\\
-6x+16y&=-10.
&(2)
\end{align*}
Adding equations $(1)$ and $(2)$, and solving for the variable gives:
\begin{align*}
0x-2y&=-1
\\
-2y&=-1
\\\\
\dfrac{-2y}{-2}&=\dfrac{-1}{-2}
\\\\
y&=\dfrac{1}{2}
.\end{align*}
Substituting $y=\dfrac{1}{2}$ in the first given equation, $2x-6y=3,$ results to
\begin{align*}
2x-6\left(\dfrac{1}{2}\right)&=3
\\\\
2x-3&=3
\\
2x&=3+3
\\
2x&=6
\\\\
\dfrac{2x}{2}&=\dfrac{6}{2}
\\\\
x&=3
.\end{align*}
With $x=3$ and $y=\dfrac{1}{2},$ the solution to the given system is the ordered pair $
\left(3,\dfrac{1}{2}\right)
$.
