Answer
$(6,10)$
Work Step by Step
We are given the system:
$\begin{cases}
\dfrac{2x}{3}+\dfrac{y}{5}=6\\
\dfrac{x}{6}-\dfrac{y}{2}=-4
\end{cases}$
We will use the addition method. Multiply Equation 1 by 5, Equation 2 by 2 and add the two equations to eliminate $y$ and determine $x$:
$\begin{cases}
5\left(\dfrac{2x}{3}+\dfrac{y}{5}\right)=5(6)\\
2\left(\dfrac{x}{6}-\dfrac{y}{2}\right)=2(-4)
\end{cases}$
$\dfrac{10x}{3}+y+\dfrac{x}{3}-y=30-8$
$\dfrac{11x}{3}=22$
$11x=66$
$x=\dfrac{66}{11}$
$x=6$
Substitute the value of $x$ in Equation 2 to determine $y$:
$\dfrac{6}{6}-\dfrac{y}{2}=-4$
$1-\dfrac{y}{2}=-4$
$\dfrac{y}{2}=1+4$
$\dfrac{y}{2}=5$
$y=5(2)$
$y=10$
The system's solution is:
$(6,10)$
