When you graph a system of linear equations, why does the intersection of the two lines represent the solution of the system?

Every point on the graph of one line has an 'x' and a 'y' that make the equation
of the line a true statement.

When there are two equations, and you're looking for the solution to both of them,
you're looking for one pair of numbers ... 'x' and 'y' ... that make both equations
true statements. 

But every pair of numbers 'x' and 'y' is a point on the graph of the line.  So the
same pair of numbers 'x' and 'y' must be a point on the graphs of both equations. 
The only point that's on the graph of both equations is the point where the graphs
of both equations intersect.

Bi’m pretty sure hope it works