If I have four unknown variables, x, y, j, and k, but know the values of x*j, y/k, and k/j, and x*j == y/k

How do I go about getting the values of the individual unknown variables?

You'll need one more equation for the four values. Right now you have three

@iiii hey thanks iii. will any equation do?

Fuck I thought I was done with middle school algebra systems of equations

Systems of equations!
I loved them 😄

@Root how much for you to do my homework. The current math teacher isn't hardcore enough. I need a professional to torture me with numbers.

let a = x*j = y/k
let b = k/j

ab = xk = y/j

since a and b are known, if you find x, you will get k = ab/x and j = a/x, y = ak = a²b/x

That's all the variables

If you know y, j = y/ab, x = a/j = a²b/y, k = y/a

In short, you need one more variable, this is not enough, but this can help you find patterns.

@theabbie thank you abbie. Figured it was going to be something like that.

Also voice-to-text insisted your handle is "applepie" and not "abbie."

@Wisecrack not any, but one that gives additional information, so that two if them cannot be reduced to just one.

Not just any extra equation will work if you want unique values of x, y, j, k.

Any (x, y) on the hyperbola xy = a²b (where a = x*j = y/k and b = k/j) will satisfy your current constraints.
For each of these (x, y), you get a (j, k).

If you want a unique set of values, the extra equation when converted in terms of x, y must intersect with the above hyperbola at only one point otherwise you would get 2 or more solutions.

Helpful answer, and I'm starting to grasp what you're explaining.

Suppose we have another unknown variable d.

We know d*y and we know d*k, but we don't obviously know d, y or k.

Additionally you know the
value of x/d

But obviously not x or d alone.