Solving Systems of Inequalities by Graphing Steps Intersecting Regions Separate Regions

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) 2

Intersecting Regions 3

Intersecting Regions (Cont.) 4

Separate Regions 5

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 6

Example of Finding Vertices 7

Solve by Elimination Example (Cont.) 8

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 9

Multiply, Then Use Elimination Example 10

Multiply, Then Use Elimination Example (Cont.) 11

Another Example  An untrue solution identifies and Inconsistent System  That means the lines won’t cross… 12