To determine which student found the correct solution to the equation \(3x - 4y = 8\), we will test each proposed solution by plugging the values of \(x\) and \(y\) into the equation.
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Student #1: Linda (1, -4) \[ 3(1) - 4(-4) = 3 - (-16) = 3 + 16 = 19 \quad \text{(not equal to 8)} \]
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Student #2: Nathan (5, 3) \[ 3(5) - 4(3) = 15 - 12 = 3 \quad \text{(not equal to 8)} \]
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Student #3: Gary (4, 1) \[ 3(4) - 4(1) = 12 - 4 = 8 \quad \text{(equal to 8, correct solution)} \]
Thus, the only student who found the correct solution is Student #3.
Student #3 is correct.