Warm-Up Exercises

Find the value of when1. =x 3.4+2x

3. Use the distributive property to rewrite as a product.

5y–xy

2. Find the value of when2

1y 4+ =y 6.

ANSWER 10

ANSWER 7

ANSWER ( )5–xy

Calculate the Value of a VariableExample 3

Find the value of y in the equation when and when .

9=3y2x +6=x – 9=x

SOLUTION

Method 1: First substitute for x. Then solve for y.

6=x –When 9=xWhen

9=3y2x + 9=3y2x +

9=3y2 +( )6– 9=3y2 +( )9

9=3y12 +– 9=3y18 +

21=3y =3y 9–

7=y =y 3–

Calculate the Value of a VariableExample 3

Method 2: First solve for y. Then substitute for x.

When 6:=x – 3=y +–3

2( )6– = 7

9:=xWhen 3=y +–3

2( )9 = 3–

9=3y2x + Write original equation.

9=3y 2x +– Subtract 2x from each side.

3=y +– x3

2Divide each side by 3.

Find the value of y in the equation 2y x 5x 6 when x 3 and when x 6.

Checkpoint

ANSWER 3; 15–

–=+ = +

=

Calculate the Value of a Variable

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 totalrevenue from the sale of the ads.

VERBALMODEL

Totalrevenue

•=Price of

half-pageads

Price offull page

ads•+

Number of

half-pageads

Number of

full-pageads

Example 4 Write an Equation with Two Variables

LABELS Total revenue R (dollars)=

Price of half-page ad 150 (dollars)=

Number of half-page ads h (ads)=

Price of full-page ad 250 (dollars)=

Number of full-page ads f (ads)=

ALGEBRAICMODEL

150hR = 250f+

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 model150hR = 250f+

Substitute 3500 for R.150h3500 = 250f+

Subtract 150h from each side.150h3500 = 250f–

Example 5 Use an Equation with Two Variables

Divide each side by 250.150h3500

= f–

250

Distributive property= f250

( )3h7050 –

Divide numerator and denominator by 50.= f

5

3h70 –

Make a table showing some values that solve the problem.

h 5 10 15 20

11 8 5 2=f5

3h70 –

ANSWER

One solution is 10 half-page ads and 8 full-page ads.

Checkpoint

2. 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

Use an Equation with Several Variables