Let's consider the following system of inequalities.
y ≤ - 0.5 x+1 y < 2x-1
We want to graph it. First, we are going to draw the boundary lines for both inequalities.
Let's now take a point that does not lie on either of the lines and see if it is a solution. If it is a solution to the inequality, we will shadow the half-plane that contains it. If it is not, we will shadow the other half-plane. Let ( 0, 0) be that point.
Inequality
Substitute
Simplify
y ≤ - 0.5x+1
0 ≤ - 0.5( 0)+1
0 ≤ 1
y < 2x-1
0 < 2( 0)-1
0 < - 1
Point (0,0) makes only the first inequality true. As a result, the solution set to the first inequality the half-plane that contains it. Conversely, the solution set to the second inequality the half-plane that does not contain it.
The area where the shaded regions overlap represents the common solutions to our system of inequalities. As a result, any point in this region is a solution. For example, point (2,-2) is a solution.
