To determine which system has the point (0, -2) as a solution, we can substitute \(x = 0\) and \(y = -2\) into each pair of equations in the systems provided.
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System: -4x + y = 6 and -5x - y = 21
- For -4x + y = 6: \[ -4(0) + (-2) = 6 \implies -2 \neq 6 \]
- For -5x - y = 21: \[ -5(0) - (-2) = 21 \implies 2 \neq 21 \] Not a solution.
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System: -4x + y = 6 and -5x + y = -2
- For -4x + y = 6: \[ -4(0) + (-2) = 6 \implies -2 \neq 6 \]
- For -5x + y = -2: \[ -5(0) + (-2) = -2 \implies -2 = -2 \] Not a solution.
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System: -3x + 6y = -12 and -5x + y = -2
- For -3x + 6y = -12: \[ -3(0) + 6(-2) = -12 \implies -12 = -12 \]
- For -5x + y = -2: \[ -5(0) + (-2) = -2 \implies -2 = -2 \] This is a solution.
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System: x + y = 2 and -x + 2y = 16
- For x + y = 2: \[ 0 + (-2) = 2 \implies -2 \neq 2 \]
- For -x + 2y = 16: \[ -0 + 2(-2) = 16 \implies -4 \neq 16 \] Not a solution.
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System: -5x = y - 3 and 3x - 8y = 24
- For -5x = y - 3: \[ -5(0) = -2 - 3 \implies 0 \neq -5 \]
- For 3x - 8y = 24: \[ 3(0) - 8(-2) = 24 \implies 16 \neq 24 \] Not a solution.
From the checks, the system where (0, -2) is a solution is:
-3x + 6y = -12 and -5x + y = -2.