Practice and Problem-Solving Exercises

A Practice

See Problems 1 and 2.

Solve each system using elimination.

7. 3 x + 3 y = 27 x − 3 y = − 11 table with 2 rows and 1 column , row1 column 1 , 3 x plus 3 y equals 27 , row2 column 1 , x minus 3 y equals negative 11 , end table
8. − x + 5 y = 13 x − y = 15 table with 2 rows and 1 column , row1 column 1 , negative x plus 5 y equals 13 , row2 column 1 , x minus y equals 15 , end table
9. 2 x + 4 y = 22 2 x − 2 y = − 8 table with 2 rows and 1 column , row1 column 1 , 2 x plus 4 y equals 22 , row2 column 1 , 2 x minus 2 y equals negative 8 , end table
10. 4 x − 7 y = 3 x − 7 y = − 15 table with 2 rows and 1 column , row1 column 1 , 4 x minus 7 y equals 3 , row2 column 1 , x minus 7 y equals negative 15 , end table
11. 5 x − y = 0 3 x + y = 24 table with 2 rows and 1 column , row1 column 1 , 5 x minus y equals 0 , row2 column 1 , 3 x plus y equals 24 , end table
12. 6 x + 5 y = 39 3 x + 5 y = 27 table with 2 rows and 1 column , row1 column 1 , 6 x plus 5 y equals 39 , row2 column 1 , 3 x plus 5 y equals 27 , end table

13. Talent Show Your school's talent show will feature 12 solo acts and 2 ensemble acts. The show will last 90 min. The 6 solo performers judged best will give a repeat performance at a second 60-min show, which will also feature the 2 ensemble acts. Each solo act lasts x minutes, and each ensemble act lasts y minutes.

    1. Write a system of equations to model the situation.
    2. Solve the system from part (a). How long is each solo act? How long is each ensemble act?

14. Furniture A carpenter is designing a drop-leaf table with two drop leaves of equal size. The lengths of the table when one leaf is folded up and when both leaves are folded up are shown. How long is the table when no leaves are folded up?

    

See Problems 3 and 4.

Solve each system using elimination.

15. 2 x + 3 y = 9 x + 5 y = 8 table with 2 rows and 1 column , row1 column 1 , 2 x plus 3 y equals 9 , row2 column 1 , x plus 5 y equals 8 , end table

16. 3 x + y = 5 2 x − 2 y = − 2 table with 2 rows and 1 column , row1 column 1 , 3 x plus y equals 5 , row2 column 1 , 2 x minus 2 y equals negative 2 , end table

17. 6 x + 4 y = 42 − 3 x + 3 y = − 6 table with 2 rows and 1 column , row1 column 1 , 6 x plus 4 y equals 42 , row2 column 1 , negative 3 x plus 3 y equals negative 6 , end table

18. 3 x + 2 y = 17 2 x + 5 y = 26 table with 2 rows and 1 column , row1 column 1 , 3 x plus 2 y equals 17 , row2 column 1 , 2 x plus 5 y equals 26 , end table

19. 6 x − 3 y = 15 7 x + 4 y = 10 table with 2 rows and 1 column , row1 column 1 , 6 x minus 3 y equals 15 , row2 column 1 , 7 x plus 4 y equals 10 , end table

20. 5 x − 9 y = − 43 3 x + 8 y = 68 table with 2 rows and 1 column , row1 column 1 , 5 x minus 9 y equals negative 43 , row2 column 1 , 3 x plus 8 y equals 68 , end table

See Problem 5.

Tell whether the system has one solution, infinitely many solutions, or no solution.

21. 9 x + 8 y = 15 9 x + 8 y = 30 table with 2 rows and 1 column , row1 column 1 , 9 x plus 8 y equals 15 , row2 column 1 , 9 x plus 8 y equals 30 , end table

22. 3 x + 4 y = 24 6 x + 8 y = 24 table with 2 rows and 1 column , row1 column 1 , 3 x plus 4 y equals 24 , row2 column 1 , 6 x plus 8 y equals 24 , end table

23. 5 x − 3 y = 10 10 x + 6 y = 20 table with 2 rows and 1 column , row1 column 1 , 5 x minus 3 y equals 10 , row2 column 1 , 10 x plus 6 y equals 20 , end table

24. 2 x − 5 y = 17 6 x − 15 y = 51 table with 2 rows and 1 column , row1 column 1 , 2 x minus 5 y equals 17 , row2 column 1 , 6 x minus 15 y equals 51 , end table

25. 4 x − 7 y = 15 − 8 x + 14 y = − 30 table with 2 rows and 1 column , row1 column 1 , 4 x minus 7 y equals 15 , row2 column 1 , negative 8 x plus 14 y equals negative 30 , end table

26. 4 x − 8 y = 15 − 5 x + 10 y = − 30 table with 2 rows and 1 column , row1 column 1 , 4 x minus 8 y equals 15 , row2 column 1 , negative 5 x plus 10 y equals negative 30 , end table

B Apply

27. Think About a Plan A photo studio offers portraits in 8 × 10 8 times 10  and wallet-sized formats. One customer bought two 8 × 10 8 times 10  portraits and four wallet-sized portraits and paid $52. Another customer bought three 8 × 10 8 times 10  portraits and two wallet-sized portraits and paid $50. What is the cost of an 8 × 10 8 times 10  portrait? What is the cost of a wallet-sized portrait?

    • Can you eliminate a variable simply by adding or subtracting?
    • If not, how many of the equations do you need to multiply by a constant?

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