WarmUp 6 3 Solving Linear Systems using Inverses

Warm-Up �

6. 3 Solving Linear Systems using Inverses Pre-Calculus

Objectives I will be able to… Solve systems of linear equations using inverse matrices. Essential Question? How do I solve linear equations using inverse matrices and a graphing calculator?

Practice Standards � CCSS. Math. Practice. MP 4 Model with mathematics. � CCSS. Math. Practice. MP 5 Use appropriate tools strategically. � CCSS. Math. Practice. MP 6 Attend to precision. � CCSS. Math. Practice. MP 8 Look for and express regularity in repeated reasoning. � CCSS. Math. Practice. MP 7 Look for and make use of structure.

Example 1: Use an inverse matrix to solve the system of equations, if possible. 2 x – y = 1 2 x + 3 y = 13

Example 2: Use an inverse matrix to solve the system of equations, if possible. 2 x + y = 9 x – 3 y + 2 z = 12 5 y – 3 z = – 11

You Try! Use an inverse matrix to solve the system of equations, if possible. 2 x – 3 y = – 7 –x – y = 1 A. (– 2, 1) B. (2, – 1) C. (– 2, – 1) D. no solution

Real World Application 1 Marquis has 22 coins that are all nickels, dimes, and quarters. The value of the coins is $2. 75. He has three fewer dimes than twice the number of quarters. How many of each type of coin does Marquis have?

Real World Application 2 Manny has downloaded three types of music: country, jazz, and rap. He downloaded a total of 24 songs. Each country song costs $0. 75 to download, each jazz song costs $1 to download, and each rap song costs $1. 10 to download. In all he has spent $23. 95 on his downloads. If Manny has downloaded two more jazz songs than country songs, how many of each kind of music has he downloaded?

Homework! �Complete 6. 3 Homework Worksheet!