Practice and Problem-Solving Exercises

A Practice

See Problems 1 and 2.

Solve each system using substitution. Check your answer.

11. x + y = 8 x plus y equals 8

    y = 3 x y equals 3 x

12. 2 x + 2 y = 38 2 x plus 2 y equals 38

    y = x + 3 y equals x plus 3

13. x + 3 = y x plus 3 equals y

    3 x + 4 y = 7 3 x plus 4 y equals 7

14. y = 8 − x y equals 8 minus x

    7 = 2 − y 7 equals 2 minus y

15. y = − 2 x + 6 y equals negative 2 x plus 6

    3 y − x + 3 = 0 3 y minus x plus 3 equals 0

16. 3 x + 2 y = 23 3 x plus 2 y equals 23

    1 2 x − 4 = y 1 half , x minus 4 equals y

17. y − 2 x = 3 y minus 2 x equals 3

    3 x − 2 y = 5 3 x minus 2 y equals 5

18. 4 x = 3 y − 2 4 x equals 3 y minus 2

    18 = 3 x + y 18 equals 3 x plus y

19. 2 = 2 y − x 2 equals 2 y minus x

    23 = 5 y − 4 x 23 equals 5 y minus 4 x

20. 4 y + 3 = 3 y + x 4 y plus 3 equals 3 y plus x

    2 x + 4 y = 18 2 x plus 4 y equals 18

21. 7 x − 2 y = 1 7 x minus 2 y equals 1

    2 y = x − 1 2 y equals x minus 1

22. 4 y − x = 5 + 2 y 4 y minus x equals 5 plus 2 y

    3 x + 7 y = 24 3 x plus 7 y equals 24

    See Problem 3.

23. Theater Tickets Adult tickets to a play cost $22. Tickets for children cost $15. Tickets for a group of 11 people cost a total of $228. Write and solve a system of equations to find how many children and how many adults were in the group.
24. Transportation A school is planning a field trip for 142 people. The trip will use six drivers and two types of vehicles: buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. Write and solve a system of equations to find how many buses and how many vans will be needed.
25. Geometry The measure of one acute angle in a right triangle is four times the measure of the other acute angle. Write and solve a system of equations to find the measures of the acute angles.

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