Answer
$\left\{\left(12,6\right)\right\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
\dfrac{1}{3}x-\dfrac{3}{2}y=-5\\
\dfrac{3}{4}x+\dfrac{1}{3}y=11
\end{cases}$
Multiply the first equation by 6 and the second equation by 12 to eliminate denominators:
$\begin{cases}
6\left(\dfrac{1}{3}x-\dfrac{3}{2}y\right)=6(-5)\\
12\left(\dfrac{3}{4}x+\dfrac{1}{3}y\right)=12(11)
\end{cases}$
$\begin{cases}
2x-9y=-30\\
9x+4y=132
\end{cases}$
Use the elimination method. Multiply the first equation by $-9$, multiply the second equation by 2, and add them to eliminate $x$ and determine $y$:
$\begin{cases}
-9(2x-9y)=-9(-30)\\
2(9x+4y)=2(132)
\end{cases}$
$\begin{cases}
-18x+81y=270\\
18x+8y=264
\end{cases}$
$-18x+81y+18x+8y=270+264$
$89y=534$
$y=\dfrac{534}{89}$
$y=6$
Determine $x$ using the first equation:
$2x-9y=-30$
$2x-9(6)=-30$
$2x-54=-30$
$2x=-30+54$
$2x=24$
$x=12$
The solution set of the system is:
$\left\{\left(12,6\right)\right\}$
