Answer
$x= 1, y= 1 \text{ or } (1, 1)$
Work Step by Step
The system of equations is given by the following two equations:
$$\begin{cases}
2x-3y=-1\hspace{20pt} (1)\\[3mm]
10x+y=11 \hspace{20pt} (2)
\end{cases}$$
Multiplying equation $(2)$ by $3$ so that the coefficients of y in the two equations are additive inverses gives:
$30x+3y=33\hspace{20pt} (1)$
$\text{Add the two equations to eliminate y}$
\[
\begin{aligned} 2x-3y&=-1 \\[2mm]
30x+3y&=33 \ \\[3mm]
\hline 32x&=32\\[2mm]
\end{aligned}
\]
Divide $32$ to both sides to obtain:
$x=1$
$\text{Substituting in equation (2) for }x=1$ gives:
$10(1)+y=11$
$10+y=11$
$y=1$
Therefore, the solution is:
$\boxed{x= 1 \hspace{20pt} y= 1}$