Multiple variables with multiple solutions I'm not sure how best to explain this so please ask questions to help clarify. I'm trying to find a solution to the following formula, where I know there are multiple "correct" solutions. Essentially I have three materials, each having a different density. They need to be mixed in some proportion to create the mean density provided. Formula for density is: $d = m/v$, or $density = {mass \over volume}$ $x$ has a mass of $8g/cm^3$ $y$ has a mass of $3g/cm^3$ $z$ has a mass of $1g/cm^3$, therefore: $m = 8x + 3y + 1z$ $v = x + y + z$ $d = 5.515g/cm^3$ $5.515 = {8x + 3y + 1z \over x + y + z}$ How do I go about solving this? I can approximate it by plugging into values randomly ($x=3, y=1, z=1$), but is there a more exacting process?

You can parametrize the solution as:

$$\left(x,y,\frac{1}{5.515-1}[(8-5.515)x+(3-5.515)y]\right)$$

where all I've done is just rearrange your equation and solve for $z$ in terms of $x,y$. In other words, any choice of $x,y$ above will give you a solution. Presumably since $x,y,z$ refer to volume, they must be non-negative for any of this to make sense.