L13 · Solve systems algebraically

1. 1.

   Solve the system:
   2x + 3y = 14
   2x + 2y = 10

   Answer. x = 1, y = 4

   Constructed so (1, 4) satisfies both equations.

2. 2.

   Solve the system:
   4x + 1y = 35
   1x + 3y = 17

   Answer. x = 8, y = 3

   Constructed so (8, 3) satisfies both equations.

3. 3.

   Solve the system:
   1x + 4y = 18
   3x + 3y = 27

   Answer. x = 6, y = 3

   Constructed so (6, 3) satisfies both equations.

4. 4.

   Solve the system:
   4x + 4y = 52
   1x + 3y = 29

   Answer. x = 5, y = 8

   Constructed so (5, 8) satisfies both equations.

5. 5.

   Solve the system:
   4x + 2y = 40
   3x + 1y = 26 Write a complete answer — Nora will compare with a partner.

   Answer. x = 6, y = 8

   Constructed so (6, 8) satisfies both equations.

6. 6.

   Solve the system:
   1x + 1y = 3
   1x + 2y = 4 Write a complete answer — Luis will compare with a partner.

   Answer. x = 2, y = 1

   Constructed so (2, 1) satisfies both equations.

7. 7.

   Solve the system:
   3x + 1y = 23
   1x + 1y = 13 Write a complete answer — Luis will compare with a partner.

   Answer. x = 5, y = 8

   Constructed so (5, 8) satisfies both equations.

8. 8.

   Solve the system:
   3x + 2y = 37
   3x + 3y = 45 Write a complete answer — Grace will compare with a partner.

   Answer. x = 7, y = 8

   Constructed so (7, 8) satisfies both equations.

9. 9.

   Solve the system:
   2x + 3y = 18
   2x + 1y = 10 Write a complete answer — Elena will compare with a partner.

   Answer. x = 3, y = 4

   Constructed so (3, 4) satisfies both equations.

10. 10.

    Solve the system:
    3x + 4y = 24
    3x + 1y = 15 Write a complete answer — Nora will compare with a partner.

    Answer. x = 4, y = 3

    Constructed so (4, 3) satisfies both equations.

11. 11.

    Think

    Sam tried this problem:
    Solve the system:
    2x + 1y = 9
    3x + 2y = 17
    Sam wrote x = 2, y = 7. That is not correct. What is the right answer?

    Answer. x = 1, y = 7

    Sam’s answer x = 2, y = 7 is off. Constructed so (1, 7) satisfies both equations.

12. 12.

    Think

    Grace tried this problem:
    Solve the system:
    3x + 2y = 16
    3x + 3y = 21
    Grace wrote x = 4, y = 5. That is not correct. What is the right answer?

    Answer. x = 2, y = 5

    Grace’s answer x = 4, y = 5 is off. Constructed so (2, 5) satisfies both equations.

Original extra practice. Keys are computed from the items, not guessed.