### Instruction: Solve the following system of equations: \begin{align*}
3x-5y&=-11,\\
7x+2y&=-12.
\end{align*}Express your answer as an ordered pair $(x,y).$.### Response: I need to find the values of $x$ and $y$ that satisfy both equations simultaneously.
One way to do that is to eliminate one of the variables by adding or subtracting the equations.
If I multiply the first equation by $2$ and the second equation by $5$, I get: \begin{align*}
6x-10y&=-22,\\
35x+10y&=-60.
\end{align*}
Now I can add these two equations to eliminate $y$: \begin{align*}
41x&=-82,\\
x&=-2.
\end{align*}
To find $y$, I can plug in $x=-2$ into either of the original equations.
I'll use the first one: \begin{align*}
3(-2)-5y&=-11,\\
-6-5y&=-11,\\
-5y&=-5,\\
y&=1.
\end{align*}
Therefore, the solution is $(-2,1)$.