To determine which of the given points is a solution to the inequality \(4x - 3y > 6\), we can substitute the coordinates of each point into the inequality and check if it holds true.
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For the point \((0, -2)\): \[ 4(0) - 3(-2) = 0 + 6 = 6 \] Since \(6 > 6\) is false, this point is not a solution.
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For the point \((2, 0)\): \[ 4(2) - 3(0) = 8 - 0 = 8 \] Since \(8 > 6\) is true, this point is a solution.
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For the point \((0, 2)\): \[ 4(0) - 3(2) = 0 - 6 = -6 \] Since \(-6 > 6\) is false, this point is not a solution.
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For the point \((-2, 0)\): \[ 4(-2) - 3(0) = -8 - 0 = -8 \] Since \(-8 > 6\) is false, this point is not a solution.
The only point that satisfies the inequality \(4x - 3y > 6\) is \((2, 0)\). Thus, the correct answer is:
O (2, 0).