3.3 solving systems of inequalities

755 views

Published on

Published in: Technology, Business
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
755
On SlideShare
0
From Embeds
0
Number of Embeds
12
Actions
Shares
0
Downloads
10
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

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.

×