Alright, let's solve this system of equations step by step.
Given equations:
[tex]\[
\begin{array}{l}
-2x + 3y = -12 \quad (1) \\
2x + y = 4 \quad (2)
\end{array}
\][/tex]
Step 1: Add the two equations to eliminate [tex]\(x\)[/tex]:
[tex]\[
(-2x + 3y) + (2x + y) = -12 + 4
\][/tex]
Combining like terms:
[tex]\[
(3y + y) = -12 + 4 \implies 4y = -8
\][/tex]
Step 2: Solve for [tex]\(y\)[/tex]:
[tex]\[
4y = -8 \implies y = \frac{-8}{4} = -2
\][/tex]
Step 3: Substitute [tex]\(y = -2\)[/tex] back into one of the original equations to solve for [tex]\(x\)[/tex].
Let's use equation (2):
[tex]\[
2x + y = 4
\][/tex]
Substitute [tex]\(y = -2\)[/tex]:
[tex]\[
2x - 2 = 4
\][/tex]
Solving for [tex]\(x\)[/tex]:
[tex]\[
2x = 4 + 2 \implies 2x = 6 \implies x = \frac{6}{2} = 3
\][/tex]
So, the solution to the system of equations is:
[tex]\[
(x, y) = (3, -2)
\][/tex]
