To check if the point (0, -2) is a solution to a given system of equations, we can substitute \( x = 0 \) and \( y = -2 \) into each equation in the provided systems.
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System:
- \( -4x + y = 6 \)
- \( -5x - y = 21 \)
Checking \( -4(0) + (-2) = 6 \) → \(-2 \neq 6\) (not a solution)
Checking \( -5(0) - (-2) = 21 \) → \(2 \neq 21\) (not a solution)
Conclusion: (0, -2) is NOT a solution for this system.
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System:
- \( -5x + y = -2 \)
- \( -3x + 6y = -12 \)
Checking \( -5(0) + (-2) = -2 \) → \(-2 = -2\) (a solution)
Checking \( -3(0) + 6(-2) = -12 \) → \(-12 = -12\) (a solution)
Conclusion: (0, -2) is a solution for this system.
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System:
- \( x + y = 2 \)
- \( -x + 2y = 16 \)
Checking \( 0 + (-2) = 2 \) → \(-2 \neq 2\) (not a solution)
Checking \( -0 + 2(-2) = 16 \) → \(-4 \neq 16\) (not a solution)
Conclusion: (0, -2) is NOT a solution for this system.
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System:
- \( -5x = y - 3 \)
- \( 3x - 8y = 24 \)
Checking \( -5(0) = -2 - 3 \) → \(0 = -5\) (not a solution)
Checking \( 3(0) - 8(-2) = 24 \) → \(16 \neq 24\) (not a solution)
Conclusion: (0, -2) is NOT a solution for this system.
Final Answer:
The point (0, -2) is a solution to the system:
- \( -5x + y = -2 \)
- \( -3x + 6y = -12 \).