To find the solution of the system of equations represented by the lines \( y = 4x - 10 \) and \( y = -2x + 8 \), we need to determine the point where these two lines intersect. This is done by setting the two equations equal to each other:
\[ 4x - 10 = -2x + 8 \]
Now, we will solve for \( x \):
- Add \( 2x \) to both sides:
\[ 4x + 2x - 10 = 8 \]
\[ 6x - 10 = 8 \]
- Add 10 to both sides:
\[ 6x = 18 \]
- Divide by 6:
\[ x = 3 \]
Now that we have found \( x = 3 \), we can substitute this value back into either of the original equations to find \( y \). Let's use the first equation:
\[ y = 4(3) - 10 \]
\[ y = 12 - 10 \]
\[ y = 2 \]
Therefore, the solution of the system of equations is the point:
\[ \boxed{(3, 2)} \]