How is the graph of x + |x| = y + |y| drawn?

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In summary, x + |x| = y + |y| is true for all values of x and y, but only if the equation 0 = 0 is satisfied.
  • #1
ialink
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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 can't find in my work. Who knows how this quadrant is found?

greetz
Ivar
 
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  • #2


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


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


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


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!
 

FAQ: How is the graph of x + |x| = y + |y| drawn?

What is the equation of the graph x + |x| = y + |y|?

The equation of the graph is x + |x| = y + |y|.

What is the shape of the graph?

The graph is a V-shaped curve with its vertex at the origin.

What does the graph represent?

The graph represents all the points (x, y) that satisfy the equation x + |x| = y + |y|.

What is the domain and range of the graph?

The domain of the graph is all real numbers and the range is all values greater than or equal to 0.

How can you solve for specific points on the graph?

You can solve for specific points on the graph by plugging in different values for x and solving for y, or vice versa. Another method is to plot multiple points and connect them to form the graph.

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