To find the solution of the system of the two linear equations \( y = 4x - 10 \) and \( y = -2x + 8 \), we can set the two equations equal to each other since both are equal to \( y \):
\[ 4x - 10 = -2x + 8 \]
Now, we will solve for \( x \):
- Add \( 2x \) to both sides:
\[ 4x + 2x - 10 = 8 \]
This simplifies to:
\[ 6x - 10 = 8 \]
- Next, add \( 10 \) to both sides:
\[ 6x = 18 \]
- Now, divide both sides by \( 6 \):
\[ x = 3 \]
With \( x = 3 \), we can now substitute this back into either of the original equations to find \( y \). Let's use the second equation:
\[ y = -2(3) + 8 \]
Calculating gives:
\[ y = -6 + 8 = 2 \]
So the solution of the system is:
\[ (x, y) = (3, 2) \]
In summary, the solution to the system of equations is:
\[ \boxed{(3, 2)} \]