Question

How do we verify( check) that the coordinates of the point of intersection is a common solution to two linear equations?

Answer 1

plug in the x into both of the equations, the y should stay the same

Answer 2

If the graphs of the equations intersect, then there is one solution that is true for both equations. ... When the lines intersect, the point of intersection is the only point that the two graphs have in common. So the coordinates of that point are the solution for the two variables used in the equations.