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Notes 7.4 – Linear Systems and Problem Solving Algebra M-2 Date: _________ Goal: Warm Up 1) Solve the linear system by graphing: 3x + y = 5 -x + y = -7 2) Solve the linear system by substitution: 4x + 3y = 31 y – 2x = 7 3) Solve the linear system by linear combination: 4) Choose any method to solve: 2x + 3y = 1 4x – 2y = 10 2x + 3y = 36 2x – y = 4 Steps for Problem Solving: 1. Define your variables IN WORDS 2. Set up two equations 3. Solve the system using any method 4. Write a sentence explaining your answer Example 1: In one week a music store sold 7 violins for a total of $1600. Two different types of violins were sold. One type cost $200 and the other type cost $300. How many of each type of violin did the store sell? Example 2: You combine two solutions to form a mixture that is 40% acid. One solution is 20% acid and the other is 50% acid. IF you have 90 milliliters of the mixture, how much of each solution was used to create the mixture? Example 3: Job A offers an annual salary of $30,000 plus a bonus of 1% of sales. Job B offers an annual salary of $24,000 plus a bonus of 2% of sales. How much would you have to sell to earn the same amount in each job? You Try: 1) A store sold 32 pairs of jeans for a total of $1050. Brand A sold for $30 per pair and Brand B sold for $35 per pair. How many of each brand were sold? 2) A 10-pound mixture of peanuts and cashews sells for $5.32 per pound. The price of peanuts is $3.60 per pound and the price of cashews is $7.90 per pound. How many pounds of each type are in the mixture? CW: p. 413 #27 – 31 all HW: 7.4 Skills Practice