Lesson 3-2 Example 1

Use substitution to solve the system of equations.

x + 4y = 26

x – 5y = –10

Solve by Using Substitution

x + 4y = 26 First equation

x = 26 – 4y Subtract 4y from each side.

Solve the first equation for x in terms of y.

Lesson 3-2 Example 1

Substitute 26 – 4y for x in the second equation and solve for y.

Solve by Using Substitution

x – 5y = –10 Second equation

26 – 4y – 5y = –10 Substitute 26 – 4y for x.

–9y = –36 Subtract 26 from each side.

y = 4 Divide each side by –9.

Lesson 3-2 Example 1

Now substitute the value for y in either of the original equations and solve for x.

Solve by Using Substitution

Answer: The solution of the system is (10, 4).

x + 4y = 26 First equation

x + 4(4) = 26 Replace y with 4.

x + 16 = 26 Simplify.

x = 10 Subtract 16 from each side.

Lesson 3-2 CYP 1

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A. A

B. B

C. C

D. D

Solve the system of equations using substitution. What is the solution to the system of equations? x – 3y = 2x + 7y = 12A. (1, 5)

B.

C. (8, 2)

D. (5, 1)

Lesson 3-2 Example 2

Lancaster Woodworkers Furniture Store builds two types of wooden outdoor chairs. A rocking chair sells for $265 and an Adirondack chair with footstool sells for $320. The books show that last month, the business earned $13,930 for the 48 outdoor chairs sold. How many of each chair were sold?

Read the Test Item

Solve by Substitution

You are asked to find the number of each type of chair sold.

Lesson 3-2 Example 2

Step 1 Define variables and write the system of equations. Let x represent the number of rocking chairs sold and y represent the number of Adirondack chairs sold.

Solve by Substitution

x + y = 48 The total number of chairs sold was 48.

265x + 320y = 13,930 The total amount earned was $13,930.

Solve the Test Item

Lesson 3-2 Example 2

Step 2 Solve one of the equations for one of the variables in terms of the other. Since the coefficient of x is 1, solve the first equation for x in terms of y.

Solve by Substitution

x + y = 48 First equation

x = 48 – y Subtract y from each side.

Lesson 3-2 Example 2

Step 3 Substitute 48 – y for x in the second equation.

Solve by Substitution

265x + 320y = 13,930 Second equation

265(48 – y) + 320y = 13,930 Substitute 48 – y for x.

12,720 – 265y + 320y = 13,930 Distributive Property

55y = 1210 Simplify.

y = 22 Divide each side by 55.

Lesson 3-2 Example 2

Step 4 Now find the value of x. Substitute the value for y into either equation.

Solve by Substitution

x + y = 48 First equation

x + 22 = 48 Replace y with 22.

x = 26 Subtract 22 from each side.

Answer: They sold 26 rocking chairs and 22 Adirondack chairs.

Lesson 3-2 CYP 2

0% 0%0%0%

A. A

B. B

C. C

D. D

A. 210 adult; 120 children

B. 120 adult; 210 children

C. 300 children; 30 adult

D. 300 children; 30 adult

AMUSEMENT PARKS At Amy’s Amusement Park, tickets sell for $24.50 for adults and $16.50 for children. On Sunday, the amusement park made $6405 from selling 330 tickets. How many of each kind of ticket was sold?