Answer
$\{(1,1)\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
2x-3y=-1\\
10x+y=11
\end{cases}$
Use the elimination method. Multiply the second equation by $3$ and add it to the first equation to eliminate $y$ and determine $x$:
$\begin{cases}
2x-3y=-1\\
3(10x+y)=3(11)
\end{cases}$
$\begin{cases}
2x-3y=-1\\
30x+3y=33
\end{cases}$
$2x-3y+30x+3y=-1+33$
$32x=32$
$x=1$
Determine $y$ using the second equation:
$10x+y=11$
$10(1)+y=11$
$10+y=11$
$y=1$
The solution set of the system is:
$\{(1,1)\}$