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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…
