To find the solution to the system of equations given by \(y_1 = -4x + 20\) and \(y_2 = 5x - 7\), we need to set the two equations equal to each other since at the point of intersection \(y_1\) and \(y_2\) will have the same value.
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Set the equations equal: \[ -4x + 20 = 5x - 7 \]
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Solve for \(x\): \[ 20 + 7 = 5x + 4x \ 27 = 9x \ x = 3 \]
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Now that we have \(x\), substitute it back into either equation to find \(y\). We'll use \(y_1\): \[ y = -4(3) + 20 \ y = -12 + 20 \ y = 8 \]
Thus, the solution to the system of equations is \((3, 8)\).
So the answer is A. (3, 8).