Zero Sum Game

Algebra Level pending

x ∣ y ∣ + y ∣ x ∣ = 0 x|y| + y|x| = 0

For any variables x x & y y satisfying the equation above, in which quadrants do the solutions lie in the x-y plane?

Q3 & Q4 Q2 & Q4 Q1 & Q3 All 4 quadrants Q1 & Q2

Worranat Pakornrat by Worranat Pakornrat , 36, Thailand

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1 solution

According to the equation above, if x x is positive, then ∣ x ∣ = x |x| = x . So when dividing x x both sides, we'll get ∣ y ∣ + y = 0 |y| + y = 0 , which means y y is negative.

Similarly, if y y is positive, we can deduce that x x will be negative.

Therefore, the quadrants, where both variables have opposite +/- signs, are the second and fourth on the x-y plane.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Slight technicality with the axis, which technically lie on multiple quadrants. Can you clear that up by improving the phrasing of the problem?

Calvin Lin Staff - 4 years, 11 months ago

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