Warm-Up Exercises Find the value of when 1. = x 3. 4 + 2x ANSWER 10 2.

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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

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 –

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

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 6 when x 3 and when x 6. + = + = – = ANSWER 3; 15 –

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

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) ALGEBRAIC MODEL 150h R = 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 model 150h R = 250f + Substitute 3500 for R. 150h 3500 = 250f + Subtract 150h from each side. 150h 3500 = 250f – 7

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

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