|x+y|=|13|
|x+4|=|14|
|x+y|=|13|
|x+4|=|14|
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.