3.3 a solving systems of inequalities
- 1. SYSTEMS OF LINEAR INEQUALITIES Today’s objective: 1. I will graph a system of three or more linear inequalities.
- 2. Solving Systems of Linear Inequalities 1. 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.
- 3. Solving Systems of Linear 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 of Linear Inequalities 3. The solution also includes points not on the line, so you need to shade the region of the graph: a) above the line for ‘y >’ or ‘y ≥’. b) below the line for ‘y <’ or ‘y ≤’.
- 5. Solving Systems of Linear Inequalities Example: a: 3x + 4y > - 4 b: x + 2y < 2 Put in Slope-Intercept Form: a) 3x + 4 y > −4 b) x + 2 y < 2 4 y > − 3x − 4 2 y < −x + 2 3 1 y > − x −1 y < − x +1 4 2
- 6. Solving Systems of Linear Inequalities Example, continued: 3 1 a : y > − x −1 b : y < − x +1 4 2 Graph each line, make dotted or solid and shade the correct area. a: b: dotted dotted shade above shade below
- 7. Solving Systems of Linear Inequalities 3 a: 3x + 4y > - 4 a : y > − x −1 4
- 8. Solving Systems of Linear Inequalities 3 a: 3x + 4y > - 4 a : y > − x −1 4 b: x + 2y < 2 1 b : y < − x +1 2
- 9. Solving Systems of Linear Inequalities a: 3x + 4y > - 4 The area between the b: x + 2y < 2 green arrows is the region of overlap and thus the solution.