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

  1. Jul 31, 2011 #1
    x + |x| = y + |y| ??

    1. The problem statement, all variables and given/known data
    Draw the graph of x + |x| = y + |y|


    3. 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: Jul 31, 2011
  2. jcsd
  3. Jul 31, 2011 #2
    Re: x + |x| = y + |y| ??

    Basically , [itex]\forall(x,y): x<0, y<0[/itex] satisfy the equation giving [itex]0=0[/itex]
     
  4. Jul 31, 2011 #3
    Re: x + |x| = y + |y| ??

    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?
     
  5. Jul 31, 2011 #4
    Re: x + |x| = y + |y| ??

    I have added the missing cases that indeed were missing. Thank you.

    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?
     
  6. Aug 1, 2011 #5
    Re: x + |x| = y + |y| ??

    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!
     
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