Solving Systems of Linear Inequalities

Steps to graphing inequalities: Sketch the graph of the corresponding linear equation. Use a dashed line for inequalities with < or >. Use a solid line for inequalities with ≤ or ≥. This separates the coordinate plane into two half planes. Shade one of the half planes Test a point in one of the half planes to find whether it is a solution of the inequality. If the test point is a solution, shade its half plane. If not shade the other half plane.

Sketch the graph of 6x + 5y ≥ 30… Graph the x- and y-intercepts: This will be a solid line. Test a point. (0,0) 6(0) + 5(0) ≥ 30 0 ≥ 30 Not a solution. Shade the side that doesn’t include (0,0). 6 4 2 -6 -4 -2 2 4 6 8 -2 -4 -6

With a linear system, you will be shading 2 or more inequalities. The solution to the system of inequalities is the section where they intersect (the area that is shaded by both) There will be many points that could be solutions within the area that is shaded by all

For example… y < 2 x > -1 y > x-2 The solution is the intersection of all three inequalities. So (0,0) and (1,1) are solutions but (0,3) is not.

Steps to Graphing Systems of Linear Inequalities Sketch the line that corresponds to each inequality. Lightly shade the half plane that is the graph of each linear inequality. (Colored pencils may help you distinguish the different half planes.) 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

Practice… y < 4 y > 1