The two equations form a system of equations, and the solutions to the system correspond to the points of intersection of the graphs. The solutions to the system can be found by elimination. Adding the two equations together gives $x + 2y + x - 2y = 6 + 4$, or $2x = 10$. Dividing both sides of this equation by 2 yields $x = 5$. Therefore, the value of $x$ is 5.