3.3 Solving Systems of Inequalities by Graphing Objectives: 1. Solve systems of inequalities by graphing 2.Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities

System of Inequalities The solution is the set of ordered pairs that satisfy all of the inequalities in the system Because inequalities are involved, there is an infinite number of solutions. The best way to represent this many solutions is graphically. Graph each line and shade according to the inequality. Helpful hints: ≥ shade above the line < ≤ shade below the line > or < dotted line ≥ ≤ solid line

Example Solve each system of inequalities by graphing. y≥2x-3 y<-x+2 (already solved for y!) The blue region represents the solution set.

Find the coordinates of the vertices of the figure formed by each system of inequalities. 2x-y≥-1 x+y≤4 x+4y≥4 Solve for y -y≥-2x-1 y≤2x+1y≤-x+4 4y≥-x+4y≥-¼x+1

Continued y≤2x+1 y≤-x+4 y≥-¼x+1 Find the solution for each pair of equations. Substitution is easy since they are already solved for y. 2x+1=-x+4 3x=3 x=1 y=2(1)+1 y=3 These lines cross at (1,3) y≤-x+4 y≥-¼x+1 -x+4= -¼x+1These 3=¾xlines 4=xcross y=-4+4at y=0 (4,0) y≤2x+1 y≥-¼x+1 2x+1=-¼x+1 2¼x=0 x=0 y=2(0)+1 These lines cross at (0,1)

Another Example y>-2 x+y≤3 Solve 2 nd equation for y y>-2 y≤-x+3 The solution in the blue region

Absolute Value Solve by graphing. y≤-x+1 |x+1|<3 Remember that an absolute value equation has 2 possible solutions. Don’t forget to flip inequality and change sign on 2 nd inequality. x+1 -3 X -4

Homework: Page 126, odd