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

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Rui on 7 Oct 2017
Commented: Rui on 10 Oct 2017
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

Kian Azami on 7 Oct 2017
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.
Rui on 10 Oct 2017
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.