when you graph a system of linear equations , why does the intersection of he two lines represent the soulution of the system

Answer 1

All of the points on the line are represented by an ordered pair of numbers.

That ordered pair of numbers are a solution to the equation of the line.

If the two lines contain the same point, the ordered pair naming it is a solution to both equations.

Answer 2

When you graph an equation, each point (x,y) on the line satisfies the equation.

Therefore, when 2 lines intersect, the co-ordinates of the intersection point satisfy BOTH equations, i.e. the intersection point represents the solution of the set.