Chapter 7.2 Notes: Solve Linear Systems by Substitution

Goal: You will solve systems of linear equations by using substitution.

• Solving a Linear System Using the Substitution Method:Step 1: Solve one of the equations for one of its variables. When possible, solve for a variable that has a coefficient of 1 or -1. Step 2: Substitute the expression from Step 1 into

the other equation and solve for the other variable. Step 3: Substitute the value from Step 2 into the revised equation from Step 1 and solve.

• Solve each system of linear equations by substitution. Then check your solution.

Ex.1: Ex.2:

Ex.3: Ex.4:

Ex.5: Ex.6:

3 2

2 11

y x

x y

2 6

4 6 4

x y

x y

2 3

3 5

y x

x y

5 12

3 5 4

x y

x y

2 5

3 10

y x

x y

3 7

2 4 0

x y

x y

Ex.7:

Ex.8: The sum of two numbers is 35. The first number is four times the second number. Find the numbers.

Ex.9: During a football game, students sell drinks and popcorn. They charge $2.50 for a bag of popcorn and $2 for a drink. The students collect $336 in sales. They sell twice as many bags of popcorn as drinks. How many bags of popcorn do they sell?

3

2 6

x y

x y

Ex.10: You have twice as many apples as oranges, and you have 12 apples and oranges altogether. How many apples and oranges do you have?

Ex.11: A group of friends take a day-long tubing trip. The rental shop charges $15 to rent a tube for a person and $7.50 to rent a “cooler” tube, which is used to carry food in a cooler. The friends spend $360 to rent a total of 26 tubes. How many of each type of tubes do they rent?