Join IDNLearn.com to access a wealth of knowledge and get your questions answered by experts. Ask anything and receive well-informed answers from our community of experienced professionals.

Which ordered pair is the solution to the system of equations?

[tex]\[
\left\{
\begin{array}{l}
x + 2y = -8 \\
y = \frac{1}{2}x - 2
\end{array}
\right.
\][/tex]

A. [tex]\((-2, -1)\)[/tex]
B. [tex]\((-2, -3)\)[/tex]
C. [tex]\((-6, -5)\)[/tex]
D. [tex]\((-4, -4)\)[/tex]


Sagot :

To determine which ordered pair is the solution to the system of equations
[tex]\[ \left\{\begin{array}{l} x + 2y = -8 \\ y = \frac{1}{2}x - 2 \end{array}\right., \][/tex]
we need to verify which pair satisfies both equations.

Let's analyze each pair one by one.

### Pair [tex]\((-2, -1)\)[/tex]

1. Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = -1\)[/tex] into the first equation [tex]\(x + 2y = -8\)[/tex]:
[tex]\[ -2 + 2(-1) = -2 - 2 = -4 \quad (\text{not } -8) \][/tex]
Hence, this pair does not satisfy the first equation.

### Pair [tex]\((-2, -3)\)[/tex]

1. Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = -3\)[/tex] into the first equation [tex]\(x + 2y = -8\)[/tex]:
[tex]\[ -2 + 2(-3) = -2 - 6 = -8 \quad (\text{correct}) \][/tex]
2. Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = -3\)[/tex] into the second equation [tex]\(y = \frac{1}{2}x - 2\)[/tex]:
[tex]\[ -3 = \frac{1}{2}(-2) - 2 = -1 - 2 = -3 \quad (\text{correct}) \][/tex]
This pair satisfies both equations.

### Pair [tex]\((-6, -5)\)[/tex]

1. Substitute [tex]\(x = -6\)[/tex] and [tex]\(y = -5\)[/tex] into the first equation [tex]\(x + 2y = -8\)[/tex]:
[tex]\[ -6 + 2(-5) = -6 - 10 = -16 \quad (\text{not } -8) \][/tex]
Hence, this pair does not satisfy the first equation.

### Pair [tex]\((-4, -4)\)[/tex]

1. Substitute [tex]\(x = -4\)[/tex] and [tex]\(y = -4\)[/tex] into the first equation [tex]\(x + 2y = -8\)[/tex]:
[tex]\[ -4 + 2(-4) = -4 - 8 = -12 \quad (\text{not } -8) \][/tex]
Hence, this pair does not satisfy the first equation.

Based on the above evaluations, the only ordered pair that satisfies both equations is:
[tex]\[ (-2, -3) \][/tex]

Thus, the solution to the system of equations is [tex]\(\boxed{(-2, -3)}\)[/tex].
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.