3.3 Graphing and Solving Systems of Linear Inequalities Algebra 2 3.3 Graphing and Solving Systems of Linear Inequalities

Learning Targets Students should be able to… Graph a system of linear inequalities to find the solution of the system Use systems of linear inequalities to solve real-life problems.

Warm-up Use substitution to solve. 𝑥+5𝑦=33 4𝑥+3𝑦=13 Use elimination to solve. 2. −2𝑥+3𝑦=−13 6𝑥+2𝑦=28

Homework Check Check 3.1 – 3.2 Worksheet Saved with other homework assignments.

Vocabulary SOLUTION: GRAPH: an ordered pair that is a solution of both inequalities. GRAPH: picture of all the solutions that work for the system.

Graphing a System of Linear Inequalities: 1. Graph the line that corresponds to the inequality. ** Remember: Use a dashed line for an inequality with < or > and a solid line for an inequality with ≤ or ≥.   2. Test a point to determine which side of the line needs shading. To help confusion, draw arrows in that direction along the line or use colored pencils. 3. Determine the region that contains the “overlap” of all of the other regions. Shade that region darker.

Colored Pencils Use a different colored pencil to graph each inequality. The graph of the system is the region common to all of the half planes. If you used colored pencils, it is the region that has been shaded with every color.

Example 1: Ex: Graph the system: 1. x > –1 y > 2x + 2

Example 1: Ex: Graph the system: 2. x > 0 y > 0 4x + 3y < 12

Example 1: Ex: Graph the system: x – 2y ≤ 3 y > 3x – 4

Example 1: Ex: Graph the system: 4. x > 5 y > 0 x < 2 2x – 3y > 12

Using Systems of Inequalities in Real Life 1. A store sells two brands of MP3 players. To meet customer demands, it is necessary to stock at least twice as many MP3 players of brand A as of brand B. It is also necessary to have at least 10 of brand B available. In the store there is room for no more than 50 players. Write and graph a system of inequalities to describe the ways to stock to brands.

Using Systems of Inequalities in Real Life 2. An arena contains 1200 seats. For an upcoming concert, tickets will be priced $12 for some seats and $10 for others. At least 500 tickets are to be priced at $10, and the total sales must be at least $7200 to make a profit. What are the possible ways to price tickets?

Homework Section 3.3 Page 159 – 160 #12 – 14, 22 – 25, 28, 34, 42, 50