To find the solution to the system of equations given by \( y = 4x - 10 \) and \( y = -2x + 8 \), we can set the two equations equal to each other since both are equal to \( y \).
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Set the equations equal: \[ 4x - 10 = -2x + 8 \]
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Solve for \( x \): \[ 4x + 2x = 8 + 10 \] \[ 6x = 18 \] \[ x = 3 \]
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Now substitute \( x = 3 \) back into either of the original equations to find \( y \). We'll use the first equation: \[ y = 4(3) - 10 \] \[ y = 12 - 10 \] \[ y = 2 \]
Thus, the solution to the system of equations is \( (3, 2) \).
In summary:
- The solution of the system is \( (3, 2) \).