# Combining Equations with different variables

#### JackM777

I have an equation showing how the failure load changes with respect to variable A when variable B is fixed. I also have an equation showing how the failure load changes with respect to variable B when variable A is fixed. How do I combine them so that I can see what the failure load is at different values of A and B?
y = -906.24A + 8685 when B is 2
y = -1059.2B + 7513.2 when A is 3

I can also get equations for:
y=...A + ... when B= 1
y=...A + ... when B= 3
y=...B + ... when A=0
y=...B + ... when A=6
(Not calculated yet)

Is it possible to develop a relationship to find what y is when for example A=4 and B=6?

#### chiro

MHF Helper
Hey JackM777.

You will need to figure out dy/dA and dy/dB or tell us how y changes with respect to a single increase in both A and B.

If changes are constant for both variables then it means that your equation will be Y = cA + dB where c and d are real numbers and A,B are the corresponding values for A and B.

#### JackM777

Hi Chiro

Thanks for your response. What you are saying definitely rings a bell from something I have covered previously.

Can you give me a simple example? The equations take a lot of effort to get and so I just want to make sure that I understand before I start.

Thanks

#### chiro

MHF Helper
Basically you are looking for the numbers c and d.

You will have a list of equations and you will know your y's and the values for A and B respectively: but c and d will be the same and you are solving for those.

See if you can list all the equations in that form first and we'll go from there.

#### HallsofIvy

MHF Helper
It looks to me like you are asking for a function of the form F(A, B)= pAB+ qA+ rB+ s for some numbers, p, q, r, and s. You say "when B= 2, F(A, 2)= -906.24A + 8685" so that pB+ q= 2p+ q= -906.25 and rB+ s= 2r+ s= 8685". Also, when A= 3, y = -1059.2B + 7513.2" so pA+ r= 3p+ r= -1059.2 and qA+ s= 3q+ s= 7513.2. That gives four equations to solve for the 4 unknowns, p, q, r, and s.