X + |x| = y + |y| ?

  • Thread starter ialink
  • Start date
  • #1
24
0
x + |x| = y + |y| ??

Homework Statement


Draw the graph of x + |x| = y + |y|


The Attempt at a Solution


x + |x| = y + |y|
2x = y + |y| for x [itex]\geq[/itex] 0
0 = y + |y| for x < 0

2x = y + |y|
2x = 2y which is x = y for y [itex]\geq[/itex] 0
2x = 0 for y < 0

0 = y + |y|
0 = 2y for y [itex]\geq[/itex] 0
0 = 0 for y < 0

The answer is the graph y = x for x > 0 which i can find in my work but it is also the entire quadrant formed by x < 0 and y < 0. That quadrant i cant find in my work. Who knows how this quadrant is found?

greetz
Ivar
 
Last edited:

Answers and Replies

  • #2
557
1


Basically , [itex]\forall(x,y): x<0, y<0[/itex] satisfy the equation giving [itex]0=0[/itex]
 
  • #3
768
4


You addressed:
x>0 and y>0
x>0 and y<0

You did not specifically address the two separate cases when x<0.
if x<0 and y>0? I know, I'm just saying make sure you've thought about it....
and x<0 and y<0?
And then of course, what about y is 0 or x is 0?
 
  • #4
24
0


You did not specifically address the two separate cases when x<0.
if x<0 and y>0? I know, I'm just saying make sure you've thought about it....
and x<0 and y<0?
And then of course, what about y is 0 or x is 0?
I have added the missing cases that indeed were missing. Thank you.

Basically , ∀(x,y):x<0,y<0 satisfy the equation giving 0=0
In reply quinzo's comment I indeed understand that for each negative value for x and y results in 0 = 0 so the entire quadrant is a valid combination of x and y.

Still I'm unsure having proved that the entire quadrant is consists of possible solutions. Though i'm Not questioning they are. Have i Proved it with the added cases?
 
  • #5
24
0


Okay thanks guys i figured it out. The values for x < 0 and y < 0 are only valid if the combination meets the requirement 0 = 0 which offcourse is for all values in this domain.

Thank you!
 

Related Threads on X + |x| = y + |y| ?

  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
23
Views
3K
  • Last Post
Replies
2
Views
820
  • Last Post
Replies
15
Views
23K
  • Last Post
Replies
3
Views
2K
Replies
8
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
9K
  • Last Post
Replies
21
Views
1K
Replies
3
Views
1K
Top