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**SYSTEMS OF LINEAR INEQUALITIES**

Solving Linear Systems of Inequalities by Graphing

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**Solving Systems of Linear Inequalities**

We show the solution to a system of linear inequalities by graphing them. This process is easier if we put the inequalities into Slope-Intercept Form, y = mx + b.

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**Solving Systems of Linear Inequalities**

Graph the line using the y-intercept & slope. If the inequality is < or >, make the lines dotted. If the inequality is < or >, make the lines solid.

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**Solving Systems of Linear Inequalities**

The solution also includes points not on the line, so you need to shade the region of the graph: above the line for ‘y >’ or ‘y ’. below the line for ‘y <’ or ‘y ≤’.

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**Solving Systems of Linear Inequalities**

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

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**Solving Systems of Linear Inequalities**

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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**Solving Systems of Linear Inequalities**

a: 3x + 4y > - 4

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**Solving Systems of Linear Inequalities**

a: 3x + 4y > - 4 b: x + 2y < 2

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**Solving Systems of Linear Inequalities**

a: 3x + 4y > - 4 b: x + 2y < 2 The area between the green arrows is the region of overlap and thus the solution.

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