# Unable to derive initial equations to solve problem with the "Method of Elimination"

I’m having a hard time solving the problem above with the “Method of Elimination”. I’m guessing that I need three equations initially, but I’m only able to derive two:

`A + B + Z = 10,000`
`0.02A + 0.03B + 0.04Z = 260`

With these two, I divide the second equation by `0.02`, which results in:

`A + 1.5B + 2Z = 13,000`.

I then subtract:

`A + B + Z = 10,000`

from it, and I’m left with

`.5B + Z = 3,000`.

And that’s where I have been stuck…

Your variable ‘C’ is the variable ‘z’ that you’re asked to solve for. ‘z’ is the amount of money in bonds. Not ‘C’.

Hey there, I’ve updated the question and labeled variable “C” as “Z” for clarity, I don’t think I follow what you are trying to say =/

The third equation you’re missing is that he put twice as much money in savings (your A) as in the Cert of Deposit (your B)
So you also have A = 2B.
Use that in your first equation (the one with A, B, and Z, to eliminate A.

Well, that’s embarrassing… I was aware that `A = 2B` but didn’t know where to use that information. Seems like we have:

Initial Equations:

{moderator edit - solution removed}

… and the rest is history!

Thank you for clarifying this, I really appreciate it! Please let me know if I can shorten this process or structure it in a more intuitive way. I was expecting to have three equations initially, all containing `A` in it. It feels to me like the third equation doesn’t really make sense as a declaration initially, but is more of an equation that emerges as you progress. But that could be the perception of a total noob (me).

If we have 3 variables, then we need 3 equations to solve.
`A: money in Savings account;`
`B: money in CDs;`
`Z: money in Bonds;`

{moderator edit: solution removed per the code of conduct}

Beautiful! Thanks for taking the time!

Welcome, but sorry I didn’t see your reply while I was editing mine.

No worries. It’s funny because I saw you typing for a little while, but there’s no way to say anything lol. But yeah, I enjoyed your perspective!

The 3rd equation in that form would be `A -2*B -0*Z = 0`

I’m deleting the solutions from this thread, because it’s part of an assignment and we can’t share the answers here.