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See the attachment.
Answer D - 1
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Bunuel
If x + |y| = 8 and |x| + y = 6, then how many pairs of (x, y) satisfy these two equations?

A. 4
B. 3
C. 2
D. 1
E. 0

Are You Up For the Challenge: 700 Level Questions
if both x and y are positive: x+y=8 , x+y=6 , no solution since a+y cant have two values
if x<0 and y>0 : x+y=8 , -x+y= 6 : y=7 and x=1 but x needs to be negative so no solution.
if x>0 and y < 0 : x-y=8 , x+y=6 : x= 7 and y= -1 which satisfies the conditions thus one solution here.
if x<0 and y<0 : x-y=8 , -x+y=6 , no solution again
thus we have only one solution
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x+|y| = 8
case 1: x+y = 8 where, y >= 0
case 2: x-y = 8 where, y < 0

|x|+y = 6
case 1: x+y = 6 where, x >= 0
case 2: y-x = 6 where, x < 0

We have 4 equations
The Only pair of equation that satisfies all the conditions is

x-y = 8 where, y < 0 &
x+y = 6 where, x >= 0

Condition: x >= 0, y < 0
By Solving: x =7 , y = -1 (Satisfies)


Option D: 1
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Hello from the GMAT Club BumpBot!

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