Answer
$(4,-2)$
Work Step by Step
We are given the system:
$\begin{cases}
2x+5y=-2\\
3x-4y=20
\end{cases}$
We will use the addition method. Multiply Equation 1 by 4, Equation 2 by 5 and add them to eliminate $y$ and determine $x$:
$\begin{cases}
4(2x+5y)=4(-2)\\
5(3x-4y)=5(20)
\end{cases}$
$\begin{cases}
8x+20y=-8\\
15x-20y=100
\end{cases}$
$8x+20y+15x-20y=-8+100$
$23x=92$
$x=\dfrac{92}{23}$
$x=4$
Substitute the value of $x$ in Equation 1 to determine $y$:
$2x+5y=-2$
$2(4)+5y=-2$
$8+5y=-2$
$5y=-10$
$y=-2$
The system's solution is:
$(4,-2)$
