To determine which system the point (0, -2) is a solution to, we need to substitute x = 0 and y = -2 into each equation of the systems provided and check if the equations hold true.
Let's analyze each system:
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System 1:
- Equation 1: \(-4(0) + (-2) = 6 \rightarrow -2 ≠ 6\) (not true)
- Equation 2: \(-5(0) - (-2) = 21 \rightarrow 2 ≠ 21\) (not true)
This system does not include the point.
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System 2:
- Equation 1: \(0 + (-2) = 2 \rightarrow -2 ≠ 2\) (not true)
- Equation 2: \(-0 + 2(-2) = 16 \rightarrow -4 ≠ 16\) (not true)
This system does not include the point.
-
System 3:
- Equation 1: \(-5(0) + (-2) = -2 \rightarrow -2 = -2\) (true)
- Equation 2: \(-3(0) + 6(-2) = -12 \rightarrow -12 = -12\) (true)
This system includes the point.
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System 4:
- Equation 1: \(-5(0) = (-2) - 3 \rightarrow 0 = -5\) (not true)
- Equation 2: \(3(0) - 8(-2) = 24 \rightarrow 16 = 24\) (not true)
This system does not include the point.
After checking all the systems, the only system where the point (0, -2) is a solution is System 3: -5x + y = -2 and -3x + 6y = -12.