To determine which ordered pair is a solution to the system of linear equations, we will substitute each pair into both equations and check if they satisfy both.
Equations:
- \( x + 3y = -4 \)
- \( y = -3x - 4 \)
Now, let's check each of the ordered pairs:
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For \( (-1, -1) \):
- Substitute into equation 1: \[ -1 + 3(-1) = -1 - 3 = -4 \quad \text{(True)} \]
- Substitute into equation 2: \[ -1 = -3(-1) - 4 \Rightarrow -1 = 3 - 4 \Rightarrow -1 = -1 \quad \text{(True)} \]
- Therefore, \( (-1, -1) \) is a solution.
-
For \( (1, 1) \):
- Substitute into equation 1: \[ 1 + 3(1) = 1 + 3 = 4 \quad \text{(False)} \]
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For \( (1, -1) \):
- Substitute into equation 1: \[ 1 + 3(-1) = 1 - 3 = -2 \quad \text{(False)} \]
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For \( (-1, 1) \):
- Substitute into equation 1: \[ -1 + 3(1) = -1 + 3 = 2 \quad \text{(False)} \]
After checking all ordered pairs, the only pair that satisfies both equations is \( (-1, -1) \).
Thus, the solution to the system of equations is: \[ \boxed{(-1, -1)} \]