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Question 2 of 5

Select the correct answer.

Solve the system of equations given below:
[tex]\[
\begin{aligned}
x + 2y &= -4 \\
2x + 3y &= 1
\end{aligned}
\][/tex]

A. [tex]\((-9, 14)\)[/tex]
B. [tex]\((-14, 9)\)[/tex]
C. [tex]\((9, -14)\)[/tex]
D. [tex]\((14, -9)\)[/tex]

Sagot :

GinnyAnswer
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]
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