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Warm Up Solve by graphing y = x + 3 2x + y = 4 2) Solve by substitution 2x + y = 5 4x + 2y = 5 3) Solve by elimination x – y = 7 3x – y = -19 Turn in stamp sheets today!

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**HW Check – 5.10 a) no solution b) no solution c) (2,3) d) (2, 2)**

2) a) (9, 28) b) n = 1, C = -3 c) a = .75, b = d) s = -3, t = 9.4 3) a) (1, 3) b) (2, -2)

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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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Examples: 4) 2x – 3y ≤ 6 **When you multiply or divide by a negative, flip the inequality sign.

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Examples: 5) 3x + 2y < -2

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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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**Let’s graph the next problem using the calculator #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: 5.11 **

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