SYSTEMS OF LINEAR INEQUALITIES Solving Linear Systems of Inequalities by Graphing

Solving Systems of Linear Inequalities 1.We show the solution to a system of linear inequalities by ___________ ________. a) This process is easier if we put the inequalities into Slope-Intercept Form, ______________.

Solving Systems of Linear Inequalities 2.Graph the line using the _________ & ___________. a)If the inequality is ___or ___, make the line dotted. b)If the inequality is ___ or ___, make the lines solid.

Solving Systems of Linear Inequalities 3.The solution also includes points not on the line, so you need to ________ the region of the graph: a) ______ the line for ‘y >’ or ‘y  ’. b) ______the line for ‘y <’ or ‘y ≤’.

Solving Systems of Linear Inequalities Example: a: 3x + 4y > - 4 b: x + 2y < 2 Put in Slope-Intercept Form:

Solving Systems of Linear Inequalities Graph each line, make dotted or solid and shade the correct area. Example, continued:

Solving Systems of Linear Inequalities a: 3x + 4y > - 4

Solving Systems of Linear Inequalities a: 3x + 4y > - 4 b: x + 2y < 2

Solving Systems of Linear Inequalities a: 3x + 4y > - 4 b: x + 2y < 2 The area between the green arrows is the region of overlap and thus the solution.

PRACTICE #1 on Worksheet  We will solve on the whiteboard together! STEP 1: REARRANGE inequalities to look like ___________ 4x + 5y ≤ 2 y ≤ x + 3

Practice (cont.) STEP 2: Graph each inequality like a linear equation. STEP 3: Shade area where point values “work” (plug in, does it make sense?)

Practice (cont.) STEP 4: FIND THE COMMONLY SHADED AREA. STEP 5: This is your final answer (only shade this part on final answer) FINAL ANSWER

PRACTICE (cont) (#2) 3x + 5y > 15y ≤ x – 2 Repeat graphing strategy (5 STEPS!)

PRACTICE Solve # 3-8 on Worksheet by graphing on your whiteboard! (worksheet should be inside communicator!)