L12 · Systems of linear equations

1. 1.

   The graphs of y = x + 2 and y = 2x + -2 intersect at one point. That point is the solution of the system. Check whether (4, 6) lies on y = x + 2.

   Answer. 4 + 2 = 6 (yes)

   Substitute x = 4: 4 + 2 = 6.

2. 2.

   The graphs of y = x + 3 and y = 2x + 0 intersect at one point. That point is the solution of the system. Check whether (3, 6) lies on y = x + 3.

   Answer. 3 + 3 = 6 (yes)

   Substitute x = 3: 3 + 3 = 6.

3. 3.

   The graphs of y = x + 4 and y = 2x + 2 intersect at one point. That point is the solution of the system. Check whether (2, 6) lies on y = x + 4.

   Answer. 2 + 4 = 6 (yes)

   Substitute x = 2: 2 + 4 = 6.

4. 4.

   The graphs of y = x + -2 and y = 2x + -5 intersect at one point. That point is the solution of the system. Check whether (3, 1) lies on y = x + -2.

   Answer. 3 + -2 = 1 (yes)

   Substitute x = 3: 3 + -2 = 1.

5. 5.

   The graphs of y = x + 4 and y = 2x + 2 intersect at one point. That point is the solution of the system. Check whether (2, 6) lies on y = x + 4. Write a complete answer — Grace will compare with a partner.

   Answer. 2 + 4 = 6 (yes)

   Substitute x = 2: 2 + 4 = 6.

6. 6.

   The graphs of y = x + 1 and y = 2x + -4 intersect at one point. That point is the solution of the system. Check whether (5, 6) lies on y = x + 1. Write a complete answer — Sam will compare with a partner.

   Answer. 5 + 1 = 6 (yes)

   Substitute x = 5: 5 + 1 = 6.

7. 7.

   The graphs of y = x + 3 and y = 2x + 1 intersect at one point. That point is the solution of the system. Check whether (2, 5) lies on y = x + 3. Write a complete answer — Owen will compare with a partner.

   Answer. 2 + 3 = 5 (yes)

   Substitute x = 2: 2 + 3 = 5.

8. 8.

   The graphs of y = x + 5 and y = 2x + 4 intersect at one point. That point is the solution of the system. Check whether (1, 6) lies on y = x + 5. Write a complete answer — Malik will compare with a partner.

   Answer. 1 + 5 = 6 (yes)

   Substitute x = 1: 1 + 5 = 6.

9. 9.

   The graphs of y = x + 2 and y = 2x + 0 intersect at one point. That point is the solution of the system. Check whether (2, 4) lies on y = x + 2. Write a complete answer — Mei will compare with a partner.

   Answer. 2 + 2 = 4 (yes)

   Substitute x = 2: 2 + 2 = 4.

10. 10.

    The graphs of y = x + 0 and y = 2x + -5 intersect at one point. That point is the solution of the system. Check whether (5, 5) lies on y = x + 0. Write a complete answer — Grace will compare with a partner.

    Answer. 5 + 0 = 5 (yes)

    Substitute x = 5: 5 + 0 = 5.

11. 11.

    Think

    Luis tried this problem:
    The graphs of y = x + -1 and y = 2x + -4 intersect at one point. That point is the solution of the system. Check whether (3, 2) lies on y = x + -1.
    Luis wrote 4 + -1 = 2 (yes). That is not correct. What is the right answer?

    Answer. 3 + -1 = 2 (yes)

    Luis’s answer 4 + -1 = 2 (yes) is off. Substitute x = 3: 3 + -1 = 2.

12. 12.

    Think

    Priya tried this problem:
    The graphs of y = x + 2 and y = 2x + -1 intersect at one point. That point is the solution of the system. Check whether (3, 5) lies on y = x + 2.
    Priya wrote 2 + 2 = 5 (yes). That is not correct. What is the right answer?

    Answer. 3 + 2 = 5 (yes)

    Priya’s answer 2 + 2 = 5 (yes) is off. Substitute x = 3: 3 + 2 = 5.

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