1. Warm-Up Exercises
Find the value of when 1. = x 3. 4 + 2x
ANSWER 10 2.
Find the value of when 2 1 y 4 + = 6.
ANSWER 7
3. Use the distributive property to rewrite as a product. 5y – xy
ANSWER ( ) 5 – x y

2. Find the value of y in the equation when and when . 9 = 3y 2x + 6 = x
Example 3
Calculate the Value of a Variable
Find the value of y in the equation when and when 9 = 3y 2x + 6 = x – 9 = x
SOLUTION
Method 1: First substitute for x. Then solve for y. 6 = x –
When 9 9 = 3y 2x + 9 = 3y 2 + ( ) 6 – 9 = 3y 12 + – 18 21 = 3y 9 – 7 = y 3 –

3. Method 2: First solve for y. Then substitute for x.
Example 3
Calculate the Value of a Variable
Method 2: First solve for y. Then substitute for x. 9 = 3y 2x +
Write original equation. 9 = 3y 2x + –
Subtract 2x from each side. 3 = y + – x 2
Divide each side by 3.
When 6: = x – 3 y + 2 ( ) 6 7 9: = x
When 3 y + – 2 ( ) 9

4. Find the value of y in the equation 2y x 5x 6 when x 3 and when x 6. +
Checkpoint
Calculate the Value of a Variable
Find the value of y in the equation 2y x 5x when x and when x + = + = – =
ANSWER
3; 15 –

5. revenue from the sale of the ads.
Example 4
Write an Equation with Two Variables
Yearbook Ads in your school’s yearbook sell for $150 per half page and $250 per full page. Write an equation with more than one variable to represent the total
revenue from the sale of the ads.
VERBAL
MODEL
Total
revenue • =
Price of
half-page
ads
full page +
Number of
Number of
full-page 5

6. Example 4 Write an Equation with Two Variables LABELS Total revenue R=
(dollars)
Price of half-page ad =
(dollars)
Number of half-page ads h
(ads) =
Price of full-page ad =
(dollars)
Number of full-page ads f =
(ads)
ALGEBRAIC
MODEL
150h R =
250f +

7. Example 5
Use an Equation with Two Variables
Yearbook The yearbook staff needs to raise an additional $3500 through the sale of ads before printing the yearbook. What are some combinations of full-page ads and half-page ads that will meet this objective?
SOLUTION
Use the algebraic model from Example 4. Substitute 3500 for R and solve for f.
Algebraic model
150h R =
250f +
Substitute 3500 for R.
150h
3500 =
250f +
Subtract 150h from each side.
150h
3500 =
250f – 7

8. Make a table showing some values that solve the problem.
Example 5
Use an Equation with Two Variables
3500 –
150h = f
Divide each side by 250.
250
Distributive property = f
250 ( ) 3h 70 50 –
Divide numerator and
denominator by 50. = f 5 3h 70 –
Make a table showing some values that solve
the problem. h 5 10 15 20 11 8 2 = f 3h 70 –
ANSWER
One solution is 10 half-page ads and 8 full-page ads. 8

9. Refer to Example 5. Suppose the goal was to sell
Checkpoint
Use an Equation with Several Variables
Refer to Example 5. Suppose the goal was to sell
$6000 worth of ads. What is one combination of
full-page and half-page ads that meets this objective?
ANSWER
Sample answer: 10 half-page ads and 18 full-page ads