solving systems of inequalities by graphing 33 22 11 steps intersecting regions separate regions

Solving Systems of Inequalities by Graphing

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1Steps

Intersecting Regions

Separate Regions

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Graphing More than One Inequality

Steps Solve for y in each equation

Do not forget the rules for solving inequalities Sign changes direction when multiplying/dividing

by a negative number Sign changes direction if you swap sides of the

variable and final answer

Graph each inequality Shade areas that satisfy BOTH inequalities

Shading is in the same area(s)

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Intersecting Regions

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Intersecting Regions (Cont.)

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Separate Regions

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Finding Vertices of a Polygonal Region

Vertices are corners of a shape Steps Given three inequalities A, B, and C

Pick any two inequalities and solve as you would equalities using the substitution or elimination methods (A & B)

Take one of the inequalities already used in the previous step and solve with the inequality not used yet (A & C)

Solve the remaining combination (B & C) The three ordered pairs obtained are the vertices

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Example of Finding Vertices

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Solve by Elimination Example (Cont.)

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Multiply, Then Use Elimination If the coefficients of either variable in the

first equation DO NOT match the corresponding coefficients in the second equation: Multiply one equation by a number that will

make one of the coefficients of a variable match in both equations

Follow the elimination steps

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Multiply, Then Use Elimination Example

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Multiply, Then Use Elimination Example (Cont.)

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Another Example

An untrue solution identifies and Inconsistent System

That means the lines won’t cross…