In order to graph a system of inequalities written in standard form, rewrite each inequality into y = mx + b form.

Example

The system of inequalities shown below is written in standard form.

3x + 4y ≥ -24
x − 5y ≥ 20

Rewrite each inequality into y = mx + b form.

3x + 4y ≥ –24
4y ≥-3x − 24
y ≥ - 3 4 x − 6

x − 5y ≥ 20
–5y ≥ -x + 20
*y ≤ 1 5 x − 4

*Reverse the inequality sign when multiplying or dividing by a negative number.

This activity might not be viewable on your mobile device. Interactive exercise. Assistance may be required. Now that the inequalities are in the form y = mx + b, use the applet to graph the system.

Look for the region that is shaded by both inequalities.

Source: Systems of Linear Inequalities Graph Applet, Ron Blond

Shown below are four tables of coordinate values.

Table A with ordered pairs (0,0), (-1,-1), (2,-1) Table B with ordered pairs (2, -5), (5, -4), (10,-3) Table C with ordered pairs (-9,-3), (0,-9), (5,1) Table D with ordered pairs (10,-5), (0,0), (0,-4)

Which table contains values of the solution region of the inequalities you just graphed?

Interactive popup. Assistance may be required.

Check Your Answer

Table BClose Pop Up

Now use the applet above to graph the system:

y ≤ 2x − 6
y ≥ 2x − 3

There is no solution to this system because there are no points on the graph that the two inequalities have in common. There is no double-shaded region. This also means that there is no single point that could be substituted in both of these inequalities and they both be true.