To find the solution of the system of equations given by \( y = 4x - 10 \) and \( y = -2x + 8 \), we can set the two equations equal to each other since they both equal \( y \):
\[ 4x - 10 = -2x + 8 \]
Now, let's solve for \( x \):
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Add \( 2x \) to both sides: \[ 4x + 2x - 10 = 8 \] \[ 6x - 10 = 8 \]
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Add \( 10 \) to both sides: \[ 6x = 18 \]
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Divide by \( 6 \): \[ x = 3 \]
Now that we have the value of \( x \), we can substitute it 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:
\[ (x, y) = (3, 2) \]
The solution is \( (3, 2) \).