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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