Answered

Solve the system of equations:

[tex]\[ y = \frac{1}{2}x - 6 \][/tex]
[tex]\[ x = -4 \][/tex]

What is the solution to the system of equations?

A. [tex]\((-8, -4)\)[/tex]
B. [tex]\((-4, -8)\)[/tex]
C. [tex]\((-4, 4)\)[/tex]
D. [tex]\((4, -4)\)[/tex]



Answer :

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]