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