To determine which ordered pair is a solution to the given system of linear equations
[tex]\[
\begin{cases}
x + 4y = 6 \\
y = -4x - 6
\end{cases}
\][/tex]
we need to check each of the provided ordered pairs to see if they satisfy both equations.
### Checking [tex]\((-2, -2)\)[/tex]:
1. Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = -2\)[/tex] into the first equation:
[tex]\[
-2 + 4(-2) = -2 - 8 = -10 \neq 6
\][/tex]
So, [tex]\((-2, -2)\)[/tex] does not satisfy the first equation.
### Checking [tex]\((-2, 2)\)[/tex]:
1. Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = 2\)[/tex] into the first equation:
[tex]\[
-2 + 4(2) = -2 + 8 = 6
\][/tex]
This satisfies the first equation.
2. Next, substitute [tex]\(x = -2\)[/tex] and [tex]\(y = 2\)[/tex] into the second equation:
[tex]\[
2 = -4(-2) - 6 = 8 - 6 = 2
\][/tex]
This satisfies the second equation as well.
Since [tex]\((-2, 2)\)[/tex] satisfies both equations, it is indeed a solution to the system.
### Checking (2, 2):
1. Substitute [tex]\(x = 2\)[/tex] and [tex]\(y = 2\)[/tex] into the first equation:
[tex]\[
2 + 4(2) = 2 + 8 = 10 \neq 6
\][/tex]
So, (2, 2) does not satisfy the first equation.
### Checking (2, -2):
1. Substitute [tex]\(x = 2\)[/tex] and [tex]\(y = -2\)[/tex] into the first equation:
[tex]\[
2 + 4(-2) = 2 - 8 = -6 \neq 6
\][/tex]
So, (2, -2) does not satisfy the first equation.
Therefore, the only ordered pair that is a solution to the system of linear equations is:
[tex]\[
\boldsymbol{(-2, 2)}
\][/tex]
This corresponds to the second choice in the list.
