Answer
$\{(2,3)\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
2x+3y-13=0\\
3x-2y=0
\end{cases}$
Bring the system to standard form:
$\begin{cases}
2x+3y=13\\
3x-2y=0
\end{cases}$
Use the elimination method. Multiply the first equation by 2, multiply the second equation by 3, and add them to eliminate $y$ and find $x$:
$2(2x+3y)+3(3x-2y)=2(13)+3(0)$
$4x+6y+9x-6y=26$
$13x=26$
$x=2$
Substitute $x=2$ in the first equation of the given system to determine $y$:
$2x+3y=13$
$2(2)+3y=13$
$4+3y=13$
$3y=9$
$y=3$
The solution set is:
$\{(2,3)\}$
