7.6 Solving Systems of Linear Inequalities

Remember How to Sketch the graph of 6x + 5y ≥ 30…

1. Write in slope- intercept form and graph:

y ≥ -6/5x + 6This will be a solid line.

2. Test a point. (0,0)6(0) + 5(0) ≥ 300 ≥ 30 Not a solution.

3. Shade the side that doesn’t include (0,0).

6

4

2

-2

-4

-6

2 4 6 8 -6 -4 -2

With a linear system, you will be shading 2 or more inequalities. Where they cross is the solution to ALL inequalities.

y < 2

x > -1

y > x-2

For example…

The solution is the intersection of all three inequalities.

So (0,0) is a solution but (0,3) is not.

Steps to Graphing Systems of Linear Inequalities

1. Sketch the line that corresponds to each inequality.2. Lightly shade the half plane that is the graph of each

linear inequality. (Colored pencils may help you distinguish the different half planes.)

3. The graph of the system is the intersection of the shaded half planes. (If you used colored pencils, it is the region that has been shaded with EVERY color.)

Practice…

y < -2x + 2

y < x + 3

y > -x - 1

y < 4

y > 1

Practice…