Alright, let's solve the system of equations step-by-step. We have the following system:
[tex]\[
\begin{cases}
4x - y = 5 \quad \text{(1)} \\
2x + y = 7 \quad \text{(2)}
\end{cases}
\][/tex]
Step 1: Add the two equations together to eliminate \(y\).
[tex]\[
(4x - y) + (2x + y) = 5 + 7
\][/tex]
[tex]\[
4x - y + 2x + y = 12
\][/tex]
[tex]\[
6x = 12
\][/tex]
Step 2: Solve for \(x\).
[tex]\[
6x = 12
\][/tex]
[tex]\[
x = 2
\][/tex]
Step 3: Substitute \(x = 2\) back into one of the original equations to solve for \(y\). We'll use equation (2):
[tex]\[
2x + y = 7
\][/tex]
[tex]\[
2(2) + y = 7
\][/tex]
[tex]\[
4 + y = 7
\][/tex]
[tex]\[
y = 3
\][/tex]
So, the solution to the system of equations is:
[tex]\[
x = 2, \quad y = 3
\][/tex]
