To determine which coordinates represent a solution to the equation \(6x - 5y = 30\), we can plug in each pair of coordinates into the equation and see if they satisfy it.
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For (0, -5): \[ 6(0) - 5(-5) = 0 + 25 = 25 \quad (\text{not } 30) \]
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For (0, -6): \[ 6(0) - 5(-6) = 0 + 30 = 30 \quad (\text{solution}) \]
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For (-5, 0): \[ 6(-5) - 5(0) = -30 - 0 = -30 \quad (\text{not } 30) \]
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For (-6, 0): \[ 6(-6) - 5(0) = -36 - 0 = -36 \quad (\text{not } 30) \]
From the calculations, the coordinate that represents a solution to the equation \(6x - 5y = 30\) is \((0, -6)\).