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Warm Up # 1 1.The perimeter of a rectangle is 32. The length is 1 more than twice the width. What are the dimensions of the rectangle? 2.Solve the system:

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Presentation on theme: "Warm Up # 1 1.The perimeter of a rectangle is 32. The length is 1 more than twice the width. What are the dimensions of the rectangle? 2.Solve the system:"— Presentation transcript:

1 Warm Up # 1 1.The perimeter of a rectangle is 32. The length is 1 more than twice the width. What are the dimensions of the rectangle? 2.Solve the system:

2 Homework Check

3 Essential Question How can we represent the solution to a system of linear inequalities?

4

5 Step 1) Put the inequalities into slope- intercept form. y = mx + b slope y-intercept We show the solution to a linear inequality with a graph.

6 Step 2)Graph the line a)If the inequality is, make the lines dotted. b)If the inequality is, make the lines solid.

7 Step 3)Shade the correct region of the graph: a) Above the line b) Below the line for y > or y .for y < or y ≤. **This is because more then 1 ordered pair can be a solution!

8 Examples: 1) y > -5x + 4

9 Examples: 2) x < 43) y ≥ -3

10

11 We show the solution to a system of linear inequalities with a graph!

12 Steps to Graphing a System of Inequalities: 1)Put the inequalities into slope- intercept form. 2)Decide if the lines should be dotted or solid 3)Shade above for y > or y , shade below for y < or y ≤. 4)Shade the overlapping section darker to show where the solutions to both inequalities lie.

13 Example #1: a: 3x + 4y > - 4 b: x + 2y < 2 Put in Slope-Intercept Form:

14 a: dotted shade above b: dotted shade below Graph each line, make dotted or solid and shade the correct area. Example, continued:

15

16 #2 Graph the system of linear inequalities. x  –1 y > x – 2

17 #3 x > -2 y -5

18 #4 y ≥ -x + 4 y < 3x - 2

19 #5 x – y > 3 7x – y ≤ -3

20 #6 7x + 2y < -10 -x + 2y ≤ 11

21 Classwork: Solving Systems of Inequalities Worksheet Homework: Unit 7 TEST -


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