#### Answer

The solution is, $\left( 4,-3 \right)$.

#### Work Step by Step

Let us consider the equation:
$2x+4y=-4$ …… (I)
$3x+5y=-3$ …… (II)
And for the addition method, the first equation (I) is multiplied by 3 and equation (II) is multiplied by $-2$ so that:
$\begin{align}
& 6x+12y=-12 \\
& -6x-10y=+6 \\
& \overline{\begin{align}
& +2y=-6 \\
& \text{ }y=-3 \\
\end{align}} \\
\end{align}$
Put $y$ into equation (I):
$\begin{align}
& 2x+4\left( -3 \right)=-4 \\
& 2x-12=-4 \\
& 2x=-4+12 \\
& 2x=8
\end{align}$
After that, simplify,
$x=4$
Hence, the values are:
$x=4,y=-3$