How to use symbolic toolbox to remove a redundant variable from the equation?

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Rui
Rui 2017-10-7
评论： Rui 2017-10-10
Dear all,
I have two equations y1 = F1(x,a,b) and y2 = F2(x,m,n), where x is an independent variable, while a, b, m and n are constants.
Assuming y1 = y2, is there a way to use symbolic toolbox to remove x from above equations, and get m and n as functions of a and b (i.e. m = G1(a,b), n = G2(a,b)) ?
Thank you!
Rui

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Kian Azami
Kian Azami 2017-10-7
maybe if you put your functions here it will be better. However, logically you have two equations and three unknowns and it is not possible to find two unknown separate than x.
Consider you find the value of x from the first equation which will be equal to something as:
x = x(y1,a,b). if y1 == y2 => x = x(y2,a,b)
Then you put this in the second equation:
y2 = F2(x(y2,a,b),m,n)
Now you only have one equation and you want to find two values which are not possible.
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Kian Azami
Kian Azami 2017-10-7
But why you don't put the whole code. I mean without the syms variable that you defined for defining the "response" the lines you put here is unreadable.
Rui
Rui 2017-10-10
Hi Kian, sorry for confusion. I have solved the issue. For sigmoid equation, (1) IC50 is defined as the C_B concentration where the response is half of the max response. (2) The max response will be reached when C_B is zero. As such, I substituted all C_B in the first equation with 0 to get the max response. Then I made max response / 2 == response, and solve for C_B. At the end, I got a C_B value where the response is half of max response, this C_B value is my IC50.

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