3.3 Solving Systems of Inequalities by graphing. Main Ideas Solve systems of inequalities by graphing. Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities.

Systems of Inequalities To solve a system of inequalities. 1. Graph the equation(s). y = mx + b y = #b x = #a Absolute value equation of a single variable. Write two equations using the rules from chapter 1. “OR” if >, ≥ “AND” if <, ≤ 2. Shading Shade each inequality individually. Where the shading overlaps is the solution. If the shading does not overlap then, no solution.

Solve each system of inequalities 1) y ≤ 3x – 42) y < 3 y > -2x + 3 x ≥ - 1

Solve each system of inequalities 3) y ≤ -¾x – 2 4) |x + 1| < 3 y ≥ -¾x + 1 y ≤ -x + 1

Vertices of a Polygonal Region How to find the vertices of a polygonal region 1. Graph each inequality to determine the region and which equations intersect. 2. Find the point of intersection for each pair of lines using one of the following methods,  Graphing – not always accurate.  Substitution  Elimination  Graphing Calculator – 2 nd, [trace], #5 intersect

Find the vertices. 1) y ≤ x2) y ≥ x – 3 y ≥ -3 y ≤ x + 7 3y + 5x ≤ 16 x + y ≤ 11 x + y ≥ -1

Rondell makes $10 an hour cutting grass and $12 an hour for raking leaves. He cannot work more than 15 hours per week. Graph two inequalities that Rondell can use to determine how many hours he needs to work at each job if he wants to earn at least $120 per week.

Jane’s band wants to spend no more that $575 recording their first CD. The studio charges at least $35 an hour to record. Graph a system of inequalities to represent this situation.