SOLUTION: Solve for x, y and z making each statement true: y > x z < y x < 0 x / z = -Z z/2 and z/3 are integers x / y = Z

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Question 1092331: Solve for x, y and z making each statement true:
y > x
z < y
x < 0
x / z = -Z

z/2 and z/3 are integers
x / y = Z
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

A very unusual kind of problem.... I hope you have shown it correctly.

You show
x%2Fz+=+-z
which means
x+=+-z%5E2 (1)

You also show
x%2Fy+=+z
which means
x+=+yz (2)

Then (1) and (2) together mean
-z%5E2+=+yz
which means
y+=+-z (3)

So y and z are opposites; and you also show that z < y. That means z is some negative number, call it -a, and y is then the positive number a. (2) then tells us that x is the negative number -a^2.

In summary, we have, where a is some positive number,
y = a
z = -a
x = -a^2

These parametric values for x, y, and z satisfy all the given conditions but one -- that z/2 and z/3 are both integers. If z/2 and z/3 are both integers, then z must be a multiple of 2*3 = 6.

So our final result is an infinite set of solutions where
y is some negative integer multiple of 6;
z is the opposite of y; and
x is the product of y and z