#### Answer

The required value is $x=-4,y=3$

#### Work Step by Step

We have to multiply the first equation with four and then add this to the second equation.
$\begin{align}
& 4\left( x+2y \right)+\left( -4x+3y \right)=4\left( 2 \right)+25 \\
& 4x+8y-4x+3y=8+25 \\
& 11y=33 \\
& y=3
\end{align}$
Substitute the value of $y=3$ in the first equation and solve for x as follows:
$\begin{align}
& x+2\left( 3 \right)=2 \\
& x+6=2 \\
& x=2-6 \\
& x=-4
\end{align}$
Thus, the value of $x=-4$ and $y=3$.