This is exactly like solving a system of inequalities. We have to understand what solving a system of equations or a system of inequalities means. It means finding a set of all points in the (x,y) plane that satisfies the constraints set by the system.
Let's say we are solving a system of equations by graphing. The point of intersection is the solution that satisfies both equations.
Let's say we are solving a system of inequalities by graphing. The shaded region is the set of all points that satisfy both inequalities. It is the intersection of the shaded region of both inequalities. I. e. the region that is common to both individual inequalities.
Now, let's say we are solving a system of inequalities where one of the inequality is actually an equation. The intersection of the two solutions would be portion of the straight line that lies in the solution region of the inequality. Here's an example.
Solve y = 2x + 3, y \leq -x + 4 . Let's look at the solution region for each equation/inequality.
Solution region for y = 2x + 3 is given by (all points on the red line):
Solution region for y \leq -x + 4 is given by (all points in the red region)
Now, the solution to the system is the set of all points that lie in both regions which is given below.
