To determine which statements about the ordered pair (−4, 0) and the system of equations are true, we need to check if this ordered pair satisfies both equations:
- First equation: \(2x + y = -8\)
- Second equation: \(x - y = -4\)
Let's substitute \((x, y) = (-4, 0)\) into both equations.
For the first equation: \[ 2(-4) + 0 = -8 \] \[ -8 + 0 = -8 \] This simplifies to: \[ -8 = -8 \quad \text{(True)} \]
For the second equation: \[ -4 - 0 = -4 \] This simplifies to: \[ -4 = -4 \quad \text{(True)} \]
Since the ordered pair \((-4, 0)\) satisfies both equations, it means:
- The ordered pair \((-4, 0)\) is a solution to the first equation because it makes the first equation true.
- The ordered pair \((-4, 0)\) is a solution to the second equation because it makes the second equation true.
- The ordered pair \((-4, 0)\) is a solution to the system because it makes both equations true.
Therefore, the true statements are:
- The ordered pair (−4, 0) is a solution to the first equation because it makes the first equation true.
- The ordered pair (−4, 0) is a solution to the second equation because it makes the second equation true.
- The ordered pair (−4, 0) is a solution to the system because it makes both equations true.
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