+23246 We will need to use these ideas: If x >= 0 then |x| = x.
If x < 0 then |x| = -x.
If y >= 0 then |y| = y.
If y < 0 then |y| = -y.
If x >= 0 and y >= 0, then: |x| + x + y = 14 ---> x + x + y = 14 ---> 2x + y = 14
x + |y| - y = 18 ---> x + y - y = 18 ---> x = 18
Solving this system, we find that x = 18 and y = -22 (but this answer is impossible because y was assumed to be >= 0.
If x >= 0 and y < 0, then |x| + x + y = 14 ---> x + x + y = 14 ---> 2x + y = 14
x + |y| - y = 18 ---> x - y - y = 18 ---> x - 2y = 18
Solving this system, we find that x = 9.2 and y = -4.4.
Now, do a similar analysis for the other two possibities (when x < 0) to get your final answer.
