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To find the solution of the system of equations given by \( y = 4x - 10 \) and \( y = -2x + 8 \), we need to set the equations equal to each other:
\[
4x - 10 = -2x + 8
\]
Now, let's solve for \( x \):
1. Add \( 2x \) to both sides:
\[
4x + 2x - 10 = 8
\]
\[
6x - 10 = 8
\]
2. Add \( 10 \) to both sides:
\[
6x = 18
\]
3. Divide by \( 6 \):
\[
x = 3
\]
Now, substitute \( x = 3 \) back into one of the original equations to find \( y \). We'll use \( y = 4x - 10 \):
\[
y = 4(3) - 10
\]
\[
y = 12 - 10
\]
\[
y = 2
\]
Thus, the solution to the system of equations is:
\[
\boxed{(3, 2)}
\]