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.
