3.3 graph systems of linear inequalities

3.3 graph systems of linear inequalities

• 1.
  SYSTEMS OF LINEAR INEQUALITIES SolvingLinear Systems of Inequalities by Graphing
• 2.
  Solving Systems ofLinear Inequalities We show the solution to a system of linear inequalities by graphing them. a) This process is easier if we put the inequalities into Slope-Intercept Form, y = mx + b. 1.
• 3.
  Solving Systems ofLinear Inequalities 2. Graph the line using the y-intercept & slope. a) If the inequality is < or >, make the lines dotted. b) If the inequality is < or >, make the lines solid.
• 4.
  Solving Systems ofLinear Inequalities 3. The solution also includes points not on the line, so you need to shade the region of the graph: above the line for ‘y >’ or ‘y ≥’. b) below the line for ‘y <’ or ‘y ≤’. a)
• 5.
  Solving Systems ofLinear Inequalities Example: a: b: 3x + 4y > - 4 x + 2y < 2 Put in Slope-Intercept Form: a) 3x + 4 y > −4 4 y > − 3x − 4 3 y > − x −1 4 b) x + 2 y < 2 2 y < −x + 2 1 y < − x +1 2
• 6.
  Solving Systems ofLinear Inequalities Example, continued: 3 a : y > − x −1 4 1 b : y < − x +1 2 Graph each line, make dotted or solid and shade the correct area. a: dotted shade above b: dotted shade below
• 7.
  Solving Systems ofLinear Inequalities a: 3x + 4y > - 4 3 a : y > − x −1 4
• 8.
  Solving Systems ofLinear Inequalities a: 3x + 4y > - 4 b: x + 2y < 2 3 a : y > − x −1 4 1 b : y < − x +1 2
• 9.
  Solving Systems ofLinear Inequalities a: 3x + 4y > - 4 b: x + 2y < 2 The area between the green arrows is the region of overlap and thus the solution.
• 10.
  Solving Systems ofLinear Inequalities a: 3x + 4y > - 4 b: x + 2y < 2 The area between the green arrows is the region of overlap and thus the solution.