To estimate the solution to the system of equations given by \( y = -x + 6 \) and \( y = 3x - 2 \), we can find the point where the two lines intersect. This point represents the solution to the system.
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Set the equations equal to each other to find the value of \( x \): \[ -x + 6 = 3x - 2 \] Rearranging gives: \[ 6 + 2 = 3x + x \] \[ 8 = 4x \] \[ x = 2 \]
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Substitute \( x = 2 \) into one of the equations to find \( y \). We can use either equation; let's use \( y = -x + 6 \): \[ y = -2 + 6 = 4 \]
Therefore, the solution to the system of equations, or the point of intersection, is \( (2, 4) \).
If you were to graph these lines, you would find that the two lines intersect at the point (2, 4).