Question 359877
5x + y = 12.
|x-y| = 6.

y = 12-5x.  This implies that |x-(12-5x)| = 6.
|x-12+5x| = 6.
|6x-12| = 6,
|x-2| = 1, after dividing both sides by 6.
Then x-2 = 1 or x-2 = -1.  The first equation gives x = 3, and the second, x = 1.  If x = 3, y = -3.  If x = 1, y = 7.  The answers are then (3,-3) or (1,7).