Certainly! Let's go through the process step-by-step to find the correct solution to the system of equations.
Given the equations:
[tex]\[ y = \frac{1}{2}x - 6 \][/tex]
[tex]\[ x = -4 \][/tex]
1. Substitute the value of [tex]\( x \)[/tex] into the equation:
We are given [tex]\( x = -4 \)[/tex]. We need to put this value into the equation [tex]\( y = \frac{1}{2}x - 6 \)[/tex] to find the corresponding value of [tex]\( y \)[/tex].
2. Calculate [tex]\( y \)[/tex]:
Replace [tex]\( x \)[/tex] with [tex]\(-4\)[/tex] in the equation:
[tex]\[
y = \frac{1}{2}(-4) - 6
\][/tex]
Simplify the expression:
[tex]\[
y = \frac{1}{2} \times -4 - 6
\][/tex]
[tex]\[
y = -2 - 6
\][/tex]
[tex]\[
y = -8
\][/tex]
3. Identify the solution:
Now that we have [tex]\( x = -4 \)[/tex] and [tex]\( y = -8 \)[/tex], let's present this as coordinates [tex]\((x, y)\)[/tex].
4. Check the options:
We have several potential solutions to choose from:
- [tex]\((-8, -4)\)[/tex]
- [tex]\((-4, -8)\)[/tex]
- [tex]\((-4, 4)\)[/tex]
- [tex]\((4, -4)\)[/tex]
From our calculations, the coordinates [tex]\((x, y) = (-4, -8)\)[/tex] match one of the provided choices.
Thus, the solution to the system of equations is:
[tex]\[
\boxed{(-4, -8)}
\][/tex]
