A linear equation can be represented by a graph of a line in the coordinate plane
All points that are on this line are solutions to the linear equation, because the ordered pair (x, y) will satisfy the equation.
For a system of linear equations, we can graph both lines in the same graph.
If the lines have an intersection point, this point will be the solution for the system, because the point in on both lines, meaning that the point is a solution for both equations at the same time.