Answer
$(2,-3)$
Work Step by Step
We are given the system:
$\begin{cases}
5x+3y=1\\
3x+4y=-6
\end{cases}$
We will use the addition method. Multiply Equation 1 by -4, Equation 2 by 3 and add the two equations to eliminate $y$ and determine $x$:
$\begin{cases}
-4(5x+3y)=-4(1)\\
3(3x+4y)=3(-6)
\end{cases}$
$\begin{cases}
-20x-12y=-4\\
9x+12y=-18
\end{cases}$
$-20x-12y+9x+12y=-4-18$
$-11x=-22$
$x=2$
Substitute the value of $x$ in Equation 1 to determine $y$:
$5x+3y=1$
$5(2)+3y=1$
$10+3y=1$
$3y=-9$
$y=-3$
The system's solution is:
$(2,-3)$
