SOLUTION: If x(x - y) = 0 and x > y, which of the following statements must be true? I. x = 0 II. y < 0 III. y - x > 0 (A) I only (B) II only (C) I and II on

Algebra ->  Inequalities -> SOLUTION: If x(x - y) = 0 and x > y, which of the following statements must be true? I. x = 0 II. y < 0 III. y - x > 0 (A) I only (B) II only (C) I and II on      Log On


   

Question 303713: If x(x - y) = 0 and x > y, which of the following statements must be true?
I. x = 0
II. y < 0
III. y - x > 0

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Well if x > y, then x%3C%3Ey. So if x%28x+-+y%29+=+0, then either x=0 or x-y=0 giving x=y. But we just said that x%3C%3Ey. So we can only say that x=0. So statement I is true.


If x=0, then just plug this value into x%3Ey to get 0%3Ey which shows us that statement II is true.


Finally, if x%3Ey, then subtracting 'x' from both sides gets us 0%3Ey-x which is the opposite of y-x%3E0. Alternatively, assume that y-x%3E0 is true. Solve for y to get y%3Ex. This is the opposite of x%3Ey. So statement III is false.