Combining Equations with different variables

Dec 2014
2
0
UK
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
Sep 2012
6,608
1,263
Australia
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.
 
Dec 2014
2
0
UK
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
Sep 2012
6,608
1,263
Australia
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
Apr 2005
20,249
7,909
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.