To determine if the point (3, -4) is a solution to the system of equations, we need to plug the values of \(x = 3\) and \(y = -4\) into both equations and see if they hold true.
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First Equation: \[ 5x + 2y = 7 \] Substitute \(x\) and \(y\): \[ 5(3) + 2(-4) = 7 \] Calculate: \[ 15 - 8 = 7 \] \[ 7 = 7 \quad \text{(True)} \]
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Second Equation: \[ 8x + 5y = 4 \] Substitute \(x\) and \(y\): \[ 8(3) + 5(-4) = 4 \] Calculate: \[ 24 - 20 = 4 \] \[ 4 = 4 \quad \text{(True)} \]
Since both equations are satisfied, (3, -4) is indeed a solution to the system of equations.