 indicates dotted/dashed line  < indicates below or to the left of the line  > indicates above or to the right of the line  If equals is part of the symbol then the line is solid

 y < -3x – 1 Start at -1 Move Down 3 and Right 1 Then shade below

 Graphing two lines or inequalities and determining their point of intersection or area of overlap (feasible region)

 y ≤ 2x  y < -1x (feasible region)

 Is (0,0) a solution of the system in the last example?  Option 1: Look at the graph. If it is in the feasible region, it is a solution for this example YES!  Option 2: use substitution ◦ 0 ≤ 2(0) + 40< -1 (0) ≤ 4 0< 4 since both are true, YES!

 Solve and graph 6< -4 – 2x < < -2x < > x > Sketch both parts Sketch the overlap Don’t forget to change the direction of the inequality

3x + y = 4 -2x + y = -1 Solve each for y y = -3x + 4 y = 2x - 1

3x + y = 4 -2x + y = -1 Solve each for y y = -3x + 4 y = 2x - 1 Enter one in Y1 the other in Y2 Press graph Press 2 nd calc Choose #5 Enter (1, 1)

3x + y = 4 -2x + y = -1 Solve one equation for y y = -3x + 4 Place the values in the other equation -2x + (-3x + 4) = -1 -2x + -3x + 4 = -1 -5x + 4 = -1 -5x = -5 x = 1

3x + y = 4 -2x + y = -1 Create a set of opposites 3x + y = 4 2x – y = 1 5x = 5 x = 1 Place the values in the other equation -2(1) + y= y = -1 y = 1