Answer
$\left\{\left(2,\dfrac{1}{2}\right)\right\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
3x-4y=4\\
x-3y=\dfrac{1}{2}
\end{cases}$
Use the elimination method. Multiply the second equation by -3 and add it to the first to eliminate $x$ and find $y$:
$3x-4y-3(x-3y)=4-3\left(\dfrac{1}{2}\right)$
$3x-4y-3x+9y=4-\dfrac{3}{2}$
$5y=\dfrac{5}{2}$
$y=\dfrac{1}{2}$
Substitute $y=\dfrac{1}{2}$ in the first equation of the given system and determine $x$:
$3x-4y=4$
$3x-4\left(\dfrac{1}{2}\right)=4$
$3x-2=4$
$3x=6$
$x=2$
The solution set is:
$\left\{\left(2,\dfrac{1}{2}\right)\right\}$
