To determine which ordered pair is a solution to the given system of linear equations:
[tex]\[
\begin{array}{l}
x + 3y = -4 \\
y = -3x - 4
\end{array}
\][/tex]
we need to check each provided ordered pair by substituting them into both equations to see which pair satisfies both equations simultaneously.
### Checking each ordered pair:
1. Pair [tex]\((-1, -1)\)[/tex]:
- Substitute [tex]\( x = -1 \)[/tex] and [tex]\( y = -1 \)[/tex] into the first equation:
[tex]\[
-1 + 3(-1) = -1 - 3 = -4
\][/tex]
This satisfies the first equation.
- Substitute [tex]\( x = -1 \)[/tex] into the second equation:
[tex]\[
y = -3(-1) - 4 = 3 - 4 = -1
\][/tex]
This satisfies the second equation.
Therefore, [tex]\((-1, -1)\)[/tex] satisfies both equations.
2. Pair [tex]\((1, 1)\)[/tex]:
- Substitute [tex]\( x = 1 \)[/tex] and [tex]\( y = 1 \)[/tex] into the first equation:
[tex]\[
1 + 3(1) = 1 + 3 = 4
\][/tex]
This does not satisfy the first equation (left-hand side is 4, not -4).
Therefore, [tex]\((1, 1)\)[/tex] is not a solution.
3. Pair [tex]\((1, -1)\)[/tex]:
- Substitute [tex]\( x = 1 \)[/tex] and [tex]\( y = -1 \)[/tex] into the first equation:
[tex]\[
1 + 3(-1) = 1 - 3 = -2
\][/tex]
This does not satisfy the first equation (left-hand side is -2, not -4).
Therefore, [tex]\((1, -1)\)[/tex] is not a solution.
4. Pair [tex]\((-1, 1)\)[/tex]:
- Substitute [tex]\( x = -1 \)[/tex] and [tex]\( y = 1 \)[/tex] into the first equation:
[tex]\[
-1 + 3(1) = -1 + 3 = 2
\][/tex]
This does not satisfy the first equation (left-hand side is 2, not -4).
Therefore, [tex]\((-1, 1)\)[/tex] is not a solution.
### Conclusion:
The only ordered pair that satisfies both equations in the system is [tex]\((-1, -1)\)[/tex]. Therefore, [tex]\((-1, -1)\)[/tex] is the solution to the system of equations.
