jmc

At the intersection of two lines, the $x$'s are equal and the $y$'s are equal. We may set $4x-19=95-2x$ to find an $x$, where the $y$'s are equal.

$$\begin{array}{rl}4x-19& =95-2x\\ 6x& =114\\ x& =\boxed{19}.\end{array}$$