Answer
$x=4$
$y=-3$
Work Step by Step
We are given the system:
$\begin{cases}
2x+4y=-4\\
3x+5y=-3
\end{cases}$
We will use the addition method. Multiply Equation 1 by -3, Equation 2 by 2, then add the two equations to eliminate $x$ and determine $y$:
$\begin{cases}
-3(2x+4y)=-3(-4)\\
2(3x+5y)=2(-3)
\end{cases}$
$\begin{cases}
-6x-12y=12\\
6x+10y=-6
\end{cases}$
$-6x-12y+6x+10y=12-6$
$-2y=6$
$y=-3$
Substitute the value of $y$ in Equation 1 to determine $x$:
$2x+4(-3)=-4$
$2x-12=-4$
$2x=8$
$x=4$
The system's solution is:
$x=4$
$y=-3$
