# Xyz=1500 what is the value of x,y and z?

Apr 28, 2018

Not enough information to determine.

#### Explanation:

The equation $x y z = 1500$ can be thought of as a system of equations. This particular system has $3$ unknowns and $1$ equation. As a result of this, there is not enough information to determine the exact values of $x , y$ and $z$.

Consider this (incorrect) argument. Let's suppose that $x = 1$, $y = 1$ and $z = 1500$. Then $x y z = \left(1\right) \left(1\right) \left(1500\right) = 1500$. This satisfies our given equation, so these must be the values of our variables.

But this is incorrect, because if $x = 10$, $y = 10$, and $z = 15$, then $x y z = \left(10\right) \left(10\right) \left(15\right) = 1500$. This still satisfies our equation, but none of the variables have the same value as previously concluded.

In general, if you have $n$ equations and $k$ unknowns with $k > n$, then there is not a unique solution to the system.