To find the value of \( x \) in the system of equations given by:
- \( y = 5x + 10 \)
- \( 6x - y = 8 \)
we can substitute the expression for \( y \) from the first equation into the second equation.
Substituting \( y = 5x + 10 \) into \( 6x - y = 8 \):
\[ 6x - (5x + 10) = 8 \]
Distributing the negative sign:
\[ 6x - 5x - 10 = 8 \]
Simplifying:
\[ x - 10 = 8 \]
Adding 10 to both sides:
\[ x = 18 \]
Thus, the value of \( x \) is \(\boxed{18}\).