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# 3.3 solving systems of inequalities

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### 3.3 solving systems of inequalities

1. 1. SYSTEMS OF LINEAR INEQUALITIESToday’s objective:1. I will graph a system of two linear inequalities.2. I will graph a system of three or more linear inequalities.
2. 2. Homework CheckWorkbook: Section 3.61. (-2, 4, 5) 2. (2, 3, -1)3. (1, 2, 3) 4. Many solutionsTextbook: Page 23434. (5, -1, 0) 35. (4, 3, 1)36. (2, -2, -5) 37. (2, 3, -2)38. (1, 3, 1) 39. (3, -2, 6)
3. 3. Solving Systems of Linear Inequalities1. 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.
4. 4. Solving Systems of Linear Inequalities2. Graph the line using the y-intercept & slope. a) If the inequality is < or >, make the lines dotted (dashed). b) If the inequality is < or >, make the lines solid.
5. 5. Solving Systems of Linear Inequalities3. 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 ≤’.
6. 6. Solving Systems of Linear InequalitiesExample: a: 3x + 4y > - 4 b: x + 2y < 2Put 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
7. 7. Solving Systems of Linear InequalitiesExample, continued: 3 1 a : y > − x −1 b : y < − x +1 4 2Graph each line, make dotted or solidand shade the correct area. a: b: dotted dotted shade above shade below
8. 8. Solving Systems of Linear Inequalities 3a: 3x + 4y > - 4 a : y > − x −1 4
9. 9. Solving Systems of Linear Inequalities 3a: 3x + 4y > - 4 a : y > − x −1 4b: x + 2y < 2 1 b : y < − x +1 2
10. 10. Solving Systems of Linear Inequalitiesa: 3x + 4y > - 4 The area between theb: x + 2y < 2 green arrows is the region of overlap and thus the solution.