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

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

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) (Show Source): You can put this solution on YOUR website!
Well if x > y, then . So if , then either or giving . But we just said that . So we can only say that . So statement I is true.

If , then just plug this value into to get which shows us that statement II is true.

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

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