Moderate# Determine when Two Lines Intersect

MVCALC-C4AXXM

Let $x=3t+1$, $y=4t-2$, and $z=5t+z_1$ be the parametric equation of a line $L$ in space.

What is the value of $z_1$ if we know that $L$ intersects the line $M$ given by the symmetric equation $x=y=z$?