From the two statement of y that has to satisfy for all values of y.

y cannot be positive and negative at the same time. The only option for y to satisfy the above equation is when y=0

Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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The definition of the absolute value |a| is 'a' when a > 0 and is ''-a' when 0 > a. Nowm for y > 0we have:

y = y ^ y = -y. There is only one solution for this. y = 0

For, 0 > t, we have:

y = -y ^ y = -(-y)

For this we have only one solution, y = 0

So, in both cases y = 0. The answer is C.

good question

A student asked me to solve this, so....

APPROACH #1: Number sense
y = |y| tells us that y is greater than or equal to 0
y = -|y| tells us that y is less than or equal to 0
Combine them to conclude that y = 0
Answer: C


APPROACH #2: Algebra
Since both given equations are set equal to y, we can write: |y| = -|y|
Add |y| to both sides of the equation to get: 2|y| = 0
Divide both sides by 2 to get: |y| = 0
Solve: y = 0
Answer: C

Cheers,
Brent

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