#### Answer

The solution of the system is $\underline{\left( 4,-2 \right)}$

#### Work Step by Step

Let us consider the system of the given equations:
$2x+5y=-2$ (I)
$3x-4y=20$ (II)
Multiply equation (I) with 4 and thus obtain
$8x+20y=-8$ (III)
Multiply equation (II) with 5 and thus obtain
$15x-20y=100$ (IV)
Add equations (III) and (IV) as follows:
$\begin{align}
& 8x+20y+15x-20y=-8+100 \\
& 23x=92 \\
& x=\frac{92}{23} \\
& x=4
\end{align}$
Put the value of x in equation (I), to obtain the value of y as shown below:
$\begin{align}
& 2\left( 4 \right)+5y=-2 \\
& 8+5y=-2 \\
& 5y=-10 \\
& y=-2
\end{align}$
Thus, the values are $ x=4$ and $ y=-2$.