7.6 Solving Systems of Linear Inequalities

Bell Work: Check to see if the ordered pairs are a solution of 2x-3y>-2 A. (0,0) B. (0,1) C. (2,-1)

Learning Targets: I can solve a system of linear inequalities by graphing. I can use a system of linear inequalities to model a real-life situation.

Remember How to Sketch the graph of 6x + 5y ≥ 30… 1.Write in slope- intercept form and graph: y ≥ - 6 / 5 x + 6 This will be a solid line. 2.Test a point. (0,0) 6(0) + 5(0) ≥ 30 0 ≥ 30 Not a solution. 3.Shade the side that doesn’t include (0,0)

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…

How is the solution of a system of linear inequalities similar to the solution of a system of linear equations? How is it different?

The solution to a system of linear inequalities must satisfy each inequality just as the solution to a system of linear equations must satisfy each equation. The solution to a system of linear inequalities is usually a region, whereas a solution to a system of linear equations is a point or a line.