7.6 Solving Systems of Linear Inequalities

43210 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will write, solve and graph systems of equations and inequalities. - Solve systems of linear equations graphically, with substitution and with elimination method. - Solve systems that have no solutions or many solutions and understand what those solutions mean. - Find where linear and quadratic functions intersect. - Use systems of equations or inequalities to solve real world problems. The student will be able to: - Solve a system graphically. - With help the student will be able to solve a system algebraically. With help from the teacher, the student has partial success with solving a system of linear equations and inequalities. Even with help, the student has no success understanding the concept of systems of equations. Focus 5 Learning Goal – (HS.A-CED.A.3, HS.A-REI.C.5, HS.A-REI.C.6, HS.A- REI.D.11, HS.A-REI.D.12): Students will write, solve and graph linear systems of equations and inequalities.

Remember How to Sketch the graph of 6x + 5y ≥ 30… 1.Graph the x- and y- intercepts: 1.(5, 0) and (0, 6) 2.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…