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

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Homework Check

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

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Graphing Linear Inequalities

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**We show the solution to a linear inequality with a graph.**

Step 1) Put the inequalities into slope-intercept form. y = mx + b slope y-intercept

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Step 2) Graph the line If the inequality is < or >, make the lines dotted. If the inequality is < or >, make the lines solid.

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**Step 3) Shade the correct region of the graph: **

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!

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Examples: 1) y > -5x + 4

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Examples: 2) x < ) y ≥ -3

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Systems of Inequalities

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

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**Steps to Graphing a System of Inequalities:**

Put the inequalities into slope-intercept form. Decide if the lines should be dotted or solid Shade above for y > or y , shade below for y < or y ≤. Shade the overlapping section darker to show where the solutions to both inequalities lie.

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

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**Graph each line, make dotted or solid and shade the correct area.**

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

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**#2 Graph the system of linear inequalities.**

x ³ –1 y > x – 2

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**#3 x > -2 y < 6 -2x + y > -5**

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#4 y ≥ -x + 4 y < 3x - 2

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#5 x – y > 3 7x – y ≤ -3

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#6 7x + 2y < -10 -x + 2y ≤ 11

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

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Entry Task Solve for y 1) 2x + -3y < 12 2) x > ½ y - 7.

Entry Task Solve for y 1) 2x + -3y < 12 2) x > ½ y - 7.

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