Review Graphing of Linear Inequality y < -3x - 1

3.3 Graphing and Solving Systems of Linear Inequalities

The following is a system of linear inequalities in two variables x + y < 6 2x – y > 4 A solution of a system of linear inequalities is an ordered pair that is a solution of each inequality in the system. For example, (3, -1) is a solution of the system above, because it makes both inequalities true. The graph of a system of linear inequalities is the graph of all solutions of the system.

Steps for Graphing 1.Graph the lines and appropriate shading for each inequality on the same coordinate plane. 2.Be sure to pay attention to whether the lines are dotted or solid. 3.The final shaded area is the section where all the shadings overlap. * Sometimes it helps to use a different colored pencil for each line and shaded region. It makes it easier to determine the overlapped shaded regions.

Graph the system y > -3x – 1 y < x Graph inequality #1 2.Graph inequality #2 3.Shade where the two shaded regions cross

Graph the system x - 2y  3 y  3x st inequality Solve for y y = ½ x – 3/2 Test point? 2 nd inequality y-int (0,-4) Slope: 3 Test point?

Graphing a System of Two Inequalities Graph the system of linear inequalities. Solid line Dotted line

Graph the system x  0 y  0 x – y  -2 1 st inequal. Vertical line 2 nd inequal. Horizontal line 3 rd inequal. y = x + 2

Graphing a system of three inequalities x > 0 y > 0 4x + 3y < 24 y = -4/3 x + 8 Test Point?

Example What is the solution of the system of inequalities? y < 3 y > |x – 1|

Exit Ticket Graph the system 1. y < x + 4 y > -2x x – y < 2 2x + y < 1