Answer
$\left( \frac{11}{5},\frac{2}{5} \right)$
Work Step by Step
$2x-y=4$ …… (1)
$x+2y=3$ …… (2)
Multiply equation $\left( 2 \right)$ by $-2$,
$\begin{align}
& x+2y=3 \\
& x\cdot \left( -2 \right)+2y\cdot \left( -2 \right)=3\cdot \left( -2 \right) \\
& -2x-4y=-6
\end{align}$ …… (3)
Add equation $\left( 1 \right)$ to equation $\left( 3 \right)$,
$\begin{matrix}
\underline{\begin{align}
& \,\,\,\,2x-y=4 \\
& -\,2x-4y=-6 \\
\end{align}} \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,-5y=-2 \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,y=\frac{2}{5} \\
\end{matrix}$
Put the value $y=\frac{2}{5}$ in the equation $\left( 2 \right)$.
$\begin{align}
& x+2y=3 \\
& x+2\left( \frac{2}{5} \right)=3 \\
& x=\frac{11}{5}
\end{align}$
Thus, $\left( x,y \right)=\left( \frac{11}{5},\frac{2}{5} \right)$.
