To find the solution to this system of equations, we need to substitute the given value of [tex]\( x \)[/tex] into the equation and solve for [tex]\( y \)[/tex].
We are given:
[tex]\[ y = \frac{1}{2} x - 6 \][/tex]
And
[tex]\[ x = -4 \][/tex]
Step-by-step solution:
1. Substitute [tex]\( x = -4 \)[/tex] into the equation [tex]\( y = \frac{1}{2} x - 6 \)[/tex].
[tex]\[
y = \frac{1}{2} (-4) - 6
\][/tex]
2. Calculate [tex]\( \frac{1}{2} (-4) \)[/tex].
[tex]\[
\frac{1}{2} \times -4 = -2
\][/tex]
3. Substitute [tex]\(-2\)[/tex] back into the equation.
[tex]\[
y = -2 - 6
\][/tex]
4. Simplify the expression.
[tex]\[
y = -2 - 6 = -8
\][/tex]
Therefore, the solution to the system of equations is [tex]\( (x, y) = (-4, -8) \)[/tex].
Checking the given options, the correct solution is:
[tex]\[
(-4, -8)
\][/tex]
So, the correct answer is:
[tex]\[ (-4, -8) \][/tex]
