Certainly! To solve the system of equations:
[tex]\[
\begin{aligned}
x + 2y &= -4 \quad \text{(Equation 1)} \\
2x + 3y &= 1 \quad \text{(Equation 2)}
\end{aligned}
\][/tex]
we can use the method of substitution or elimination. Here’s the detailed step-by-step solution:
1. Multiply Equation 1 by 2 to facilitate elimination:
[tex]\[
2(x + 2y) = 2(-4) \implies 2x + 4y = -8 \quad \text{(Equation 3)}
\][/tex]
2. Subtract Equation 2 from Equation 3 to eliminate [tex]\(2x\)[/tex]:
[tex]\[
(2x + 4y) - (2x + 3y) = -8 - 1 \\
2x + 4y - 2x - 3y = -9 \\
y = -9
\][/tex]
3. Substitute [tex]\(y = -9\)[/tex] back into Equation 1 to find [tex]\(x\)[/tex]:
[tex]\[
x + 2(-9) = -4 \\
x - 18 = -4 \\
x = -4 + 18 \\
x = 14
\][/tex]
So, the solution to the system of equations is:
[tex]\[
(x, y) = (14, -9)
\][/tex]
Hence, the correct answer is:
[tex]\[
(14, -9)
\][/tex]
