How Do You Solve for Z in Terms of X and Y?

[Gazarai]

Well, okay. I have this system of equations, kind of. Rather than looking for a number, though, I'm looking for a function. I'll try to explain myself as best as I can, but I'm not really familiar with the terms I should probably be using.

Basically, x and y are on the left side of this function, and z (and z alone; the idea is to solve for z in terms of x and y, I guess) is on the right side. Basically, I need a formula/formulas that will solve for z in terms of x and y for ALL of these sets of numbers, and if there are multiple formulas, I guess I need to know how many there are so I can find them all.

Once again, sorry if I'm not explaining myself adequately, I'll do what I can to help clear things up if you have questions.

| x | y | z |
| 2 | 2 | 2 |
| 2 | 3 | 3 |
| 3 | 2 | 3 |
| 2 | 5 | 5 |
| 5 | 2 | 5 |
| 2 | 7 | 7 |
| 7 | 2 | 7 |
| 2 | 11 | 11 |
| 11 | 2 | 11 |
| 3 | 3 | 7 |
| 3 | 5 | 13 |
| 5 | 3 | 13 |
| 3 | 7 | 19 |
| 7 | 3 | 19 |
| 3 | 11 | 29 |
| 11 | 3 | 29 |
| 5 | 5 | 23 |
| 5 | 7 | 37 |
| 7 | 5 | 37 |
| 5 | 11 | 47 |
| 11 | 5 | 47 |
| 7 | 7 | 53 |
| 7 | 11 | 71 |
| 11 | 7 | 71 |
| 11 | 11 | 97 |​

Edit: Okay, I don't think this is a system of equations, but it's kind of like that. I don't know what to call it, so I don't know how to google it and figure out how to solve something like this. How do I solve this?!

 

[Valkarie]

It looks like you are trying to solve for z in terms of x and y. It looks like the relationship between x, y and z is z = x + y^2. In other words, for each set of x and y values, z is equal to x plus y squared. For example, when x = 5 and y = 2, z = 5 + 2^2 = 5 + 4 = 9. This is the same for all of the sets of x and y values listed above.