Which ordered pair is a solution to the system of linear equations?

x + 3y = −4
y = −3x − 4
(−1, −1)
(1, 1)
(1, −1)
(−1, 1)

1 answer

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:

  1. \( x + 3y = -4 \)
  2. \( y = -3x - 4 \)

Now, let's check each of the ordered pairs:

  1. 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.
  2. For \( (1, 1) \):

    • Substitute into equation 1: \[ 1 + 3(1) = 1 + 3 = 4 \quad \text{(False)} \]
  3. For \( (1, -1) \):

    • Substitute into equation 1: \[ 1 + 3(-1) = 1 - 3 = -2 \quad \text{(False)} \]
  4. 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: \[ \boxed{(-1, -1)} \]