Answer:
To solve the system of equations using the elimination method, you want to eliminate one of the variables by adding or subtracting the equations. Let's eliminate one variable by adding the two equations:
\[
\begin{align*}
-3x + 5y &= -19 \\
2x + y &= 4 \\
\end{align*}
\]
Multiply the second equation by 5 so that the coefficients of \(y\) in both equations will cancel each other out when summed:
\[
\begin{align*}
-3x + 5y &= -19 \\
10x + 5y &= 20 \\
\end{align*}
\]
Now, add the two equations:
\[
-3x + 5y + 10x + 5y = -19 + 20
\]
Combine like terms:
\[
7x + 10y = 1
\]
Now you have one equation with one variable. Solve for either \(x\) or \(y\). Once you find one variable, substitute it back into one of the original equations to find the other variable.