This made me think a bit. Good question indeed.Please tag the source too.
a y >= |x| gives positive values for y
y <= -|x| gives negative values for y
hence there is no single value of y which satisfies the equation when you plot on a number line ,Other than x=y=0.
thus y = 0. Sufficient.
b -|y| <= x <= |y| gives
for y = 1, range for x is -1<=x <= 1
for y = 2, range for x is -2<=x <= 2 On number line.
hence many values satisfy the equation for x and y. not sufficient.
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