solve for y using the following matrix equation

Question

|x+y|=|13|

|x+4|=|14|

Answer 1

First eqaution means two possibilities:  x+y = 13  or  x+y = -13. The secoind one involves two options:

             x- 4 = 14 or x- 4 = -14. Let's comsider all options.

1) x+y = 13

    x- 4 = 14     Evidently that x = 14 +4 = 18. Then y = 13 - 18 = -5.   (18, 5)

2) x+ y = -13

    x - 4 = -14    Evidently that x = -14 + 4 = -10. Then y = -13 - (-10) = -3.   (-10, - 3)

3) x + y = 13

    x - 4 = - 14   Again, x = -10. Then y = 13-(-10) = 23.           (-10, 23)

4) x + y = - 13

    x - 4 = 14        Then x = 18, and y = -13 - 18 = -31             (18, -31).

These are all possible solutions  for the system.