Name Date Teacher Practice A. Determine whether each ordered pair is a solution of y = x (3, 8) 2. (5, 11) 3. (13, 7) 4.

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1 8 Practice A Ordered Pairs Determine whether each ordered pair is a solution of y = x (, 8). (5, ). (, 7). (9, 5) Determine whether each ordered pair is a solution of y = x (, ) 6. (, 6) 7. (5, ) 8. (9, 9) Complete the table. 9. y = x + for x =,,,, x x + y (x, y). y = 7 + x for x =,,,, x 7 + x y (x, y). y = x for x =,,,, 5 x x y (x, y) 5. y = x for x =,,,, 5. To become a member at a gym, you must pay a start-up fee of $ plus $5 each month. The equation that gives the total amount t spent on the gym is t = + 5m where m is the number of months as a member. What is the total amount spent on the gym for someone that has been a member for months? x x y (x, y) 5 8 SR

2 8 Practice B Ordered Pairs Determine whether each ordered pair is a solution of y = + x.. (, ). (, 8). (, ). (8, ) Determine whether each ordered pair is a solution of y = x. 5. (, ) 6. (, 7) 7. (5, 5) 8. (6, 6) Use the given values to complete the table of solutions. 9. y = x + 5 for x =,,,, x x + 5 y (x, y). y = x + 6 for x =,,,, x x + 6 y (x, y). y = x + for x =,,,, 5 x x + y (x, y) 5. y = x for x =,, 6, 8,. Alexis opened a savings account with a $ deposit. Each week she will put $ into the account. The equation that gives the total amount t in her account is t = + w, where w is the number of weeks since she opened the account. How much money will Alexis have in her savings account after 5 weeks? x x y (x, y) SR

3 8 Practice C Ordered Pairs Determine whether each ordered pair is a solution of y = 6x.. (, ). (, 8). (5, ). (7, 8) Use the given values to complete the table of solutions. 5. y = x + 5 for x =,,, x x + 5 y (x, y) 7. y = + x for x =,,, x + x y (x, y) 9. y = 5x for x =,,, 5 x 5x y (x, y) 5 6. y = x + 9 for x =,,, x x + 9 y (x, y) 8. y = x 5 for x =,, 6, 8 x x 5 y (x, y) 6 8. y = 8x for x =,, 6, 8 x 8x y (x, y). Each hour Maggie baby-sits she charges $ plus $.75 for each child. Write an equation for Maggie s hourly rate h in terms of the number of children c. Then solve the equation to find the hourly rate when Maggie baby-sits children SR

4 8 Review for Mastery Ordered Pairs An ordered pair can be used to write a solution for a two-variable equation. For the equation y = x + 5, a solution is (, 5). When the x-value is, the y-value is 5. x-value Which of the ordered pairs (5, ) or (, 5) is a solution of y = x? y = x y = x =? (5) Substitute 5 for x 5 =? () Substitute for x and for y. and 5 for y. =? 5 =? = 5 So, (5, ) is not a solution So, (, 5) is a solution of y = x. of y = x. (, 5) y-value Determine whether each ordered pair is a solution of the given equation. Write is or is not.. y = x + ; (, 6). y = x + ; (, ). y = x + ; (, ). y = 5x; (, 5) 5. y = x ; (5, ) 6. y = 6 x; (, ) A two-variable equation has infinitely many solutions. Use a table to find and record some solutions to a given equation. Use x =,, and, for example, to make a table of values for y = 5x. Substitute each given value of x in the expression for x. Evaluate the expression to find the value of y that completes the ordered pair. x 5x 9 = y (x, y) 5() = (, ) 5() = 9 (, 9) 5() = (, ) Complete each table. 7. y = x x x = y (x, y) () = (, ) ( ) = (, ) ( ) = (, ) 8. y = 5x x 5x = y (x, y) 5( ) = (, ) 5( ) = (, ) 5( ) = (, ) 8 SR

5 8 Challenge --, x-y-z The solution of a three-variable equation is written as an ordered triple. For example, (x, y, z) represents a solution of the equation x + y + 7z =. You can verify that (,, ) is a solution of x + y + 7z = by substituting x =, y = and z =. Arrange the numbers of the given ordered triple so that the result is a solution of the given equation.. (,, 8). (7,, ). (,, ) 5x + 8y z = 6 x + 5y z = 8 7x y + z =.,, 5.,, 6., 5, x + 9y + 8z = 5x y + z = 7 x + y z = 9 Determine the value of the indicated variable(s) so that the resulting ordered triple is a solution of the given equation. 7. (x,, 5) 8. (, y, ) 9. (,, z) x 6y + z = 5x y + z = 9 x + 5y + 8z = 7. (x, y, ). (x, 8, z). (, y, z) 7x + 5y z = 5 x + y 5z = 5 x y z = 8 SR

6 8 Problem Solving Ordered Pairs Use the table at the right for Exercises.. Write the ordered pair that shows the average miles per gallon in 99.. The data can be approximated by the equation m =.887x 595 where m is the average miles per gallon and x is the year. Use the equation to find an ordered pair (x, m) that shows the estimated miles per gallon in the year. Average Miles per Gallon Year Miles per Gallon For Exercises use the equation F =.8C +, which relates Fahrenheit temperatures F to Celsius temperatures C.. Write ordered pair (C, F) that shows the Celsius equivalent of 86 F.. Write ordered pair (C, F) that shows the Fahrenheit equivalent of C. Choose the letter for the best answer. 5. A taxi charges a $.5 flat fee plus $. per mile. Use an equation for taxi fare t in terms of miles m. Which ordered pair (m, t) shows the taxi fare for a -mile cab ride? A (, 6.9) C (, 9.) B (, 8.5) D (, 6.) 7. Maria pays a monthly fee of $.95 plus $. per minute for longdistance calls. Use an equation for the phone bill p in terms of the number of minutes m. Which ordered pair (m, p) shows the phone bill for minutes? A (, 5.95) C (, 8.) B (, 7.) D (, 86.) 6. The perimeter p of a square is four times the length of a side s, or p = s. Which ordered pair (s, p) shows the perimeter for a square that has sides that are 5 in.? F (5,.5) H (5, 9) G (5, ) J (5, 5) 8. Tickets to a baseball game cost $ each, plus $ each for transportation. Use an equation for the cost c of going to the game in terms of the number of people p. Which ordered pair (p, c) shows the cost for 6 people? F (6, 7) H (6, 8) G (6, 96) J (6, ) 8 SR

7 8 Name Date Teacher Reading Strategies Understanding Relationships The table shows the number of cartons and the number of eggs that are in each carton. Number of Cartons Number of Eggs How many eggs are there in one carton?. How many eggs are there in cartons?. If you had 6 eggs, how many cartons would that be? You can show the relationship between the number of cartons and the number of eggs as an ordered pair. For example: (, ) is the ordered pair which stands for egg carton, eggs. An ordered pair has two numbers, and they must be placed in the correct order.. Write the ordered pair for egg cartons and 6 eggs. 5. Write the ordered pair for 5 egg cartons and 6 eggs. Write true or false. 6. The ordered pair for 6 egg cartons and 7 eggs is (7, 6). 7. The ordered pair for egg cartons and eggs is (, ). Write ordered pairs for the following. 8. One deck of cards contains 5 cards. 9. Two packs of soda contain cans.. Three packages of gum contain 5 pieces. 8 SR

8 8 Puzzles, Twisters & Teasers Carnival Trivia Superman: The Escape, Tower of Terror, Goliath, Titan and Millennium Force are all? Determine whether each ordered pair is a solution of the equation. Circle the correct letter. To check your answers and to reveal the answer to the trivia question, write the letter of your answer in the decoder below. Equation Ordered Pair Yes No. x + = y (, 7) A O. 6x + = y (, 9) B D. x + = y (, 5) L N. x + = y (, 8) F P 5. x = y (, ) R L 6. 6 x = y (5, ) E I 7. x = y (5, 5) Y M 8. x = y (, ) Q S 9. x = y (6, 5) W X. (x 5) = y (6, ) C K. x = y (, 7) E T. (x 7) = y (8, ) A G They are SR

9 Answers LESSON - Practice A. no. yes. no. yes 5. no 6. no 7. yes 8. yes x x + y (x, y) + (, ) + 5 (, 5) + 6 (, 6) + 7 (, 7) + 8 (, 8) x x y (x, y) () (, ) () 6 (, 6) () 9 (, 9) () (, ) 5 (5) 5 (5, 5) x 7 + x y (x, y) (, 7) (, 8) (, 9) 7 + (, ) 7 + (, ) x x y (x, y) () (, ) () 7 (, 7) () (, ) CODE 8. $75 Practice B () 5 (, 5) 5 (5) 9 (5, 9). no. yes. yes. no 5. yes 6. yes 7. no 8. yes x x + 5 y (x, y) (, 5) (, 6) (, 7) (, 8) (, 9) x x + y (x, y) () + (, ) () + 7 (, 7) () + (, ) () + (, ) 5 (5) + 6 (5, 6) x x + 6 y (x, y) () (, 6) () (, 8) () + 6 (, ) () + 6 (, ) () + 6 (, ) x x y (x, y) () 6 (, 6) () (, ) 8 SR

10 . $ Practice C 6 (6) (6, ) 8 (8) (8, ) () 8 (, 8). yes. no. no. yes x x + 5 y (x, y) () (, 5) () (, 7) () (, 9) () + 5 (, ) x x + 9 y (x, y) () (, 9) () + 9 (, ) () (, 5) () (, 8) x + x y (x, y) + () 5 (, 5) + () 7 (, 7) + () 9 (, 9) + () (, ) x x 5 y (x, y) () 5 (, ) () 5 (, ) 6 (6) 5 9 (6, 9) 8 (8) 5 7 (8, 7) x 5x y (x, y) 5() (, ) 5() 5 (, 5) 5() (, ) 5 5(5) 5 (5, 5). x 8x y (x, y) 8() (, ) 8() (, ) 6 8(6) 6 (6, 6) 8 8(8) 5 (8, 5). h = +.75c; $.5 Review for Mastery. is not. is. is not. is 5. is not 6. is 7. x x = y (x, y) () = (, ) () = (, ) () = 8 (, 8) 8. x 5x = y (x, y) 5() = (, ) 5() = 7 (, 7) 5() = (, ) Challenge. (, 8, ). (,, 7). (,, ).,, 5. 5,, 6.,, 7. (,, 5) 8. (,, ) 9. (,, ). Possible answers are given.. (, 5, ). (, 8, ) 8 SR

11 . (,, ) Problem Solving. (99,.). (, 8.9). (, 86). (, 7.6) 5. C 6. G 7. A 8. H Reading Strategies (, 6) 5. (5, 6) 6. false 7. true 8. (, 5) 9. (, ). (, 5) Puzzles, Twisters & Teasers. O. B. L. P 5. R 6. E 7. Y 8. S 9. W. C. T. A R O L L E R C O A S T E R S 8 SR