# Rearrange Variables in an equation

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Mech Princess on 20 Jul 2012
Commented: Star Strider on 29 Jan 2023
I declare the variables using sym or syms then i have an equation a+2*b=1; I want MATLAB to give me a=1-2*b; or alternatively b=(1-a)/2;
is there a way to do this?
Also, There maybe more than 2 variables Equation maybe linear or non-linear Equation can change at each iteration. Thanks
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### Accepted Answer

Star Strider on 20 Jul 2012
Edited: Star Strider on 20 Jul 2012
This is one way:
syms a b
eqn = (a + 2*b == 1)
v_a = solve(eqn, a)
v_b = solve(eqn, b)
producing this output:
v_a =
1 - 2*b
v_b =
1/2 - a/2
I suggest you avoid expressions such as:
[a b] = solve(eqn, a, b)
even though it is valid syntax, because instead of solving the equation for ‘a’ and then solving it independently for ‘b’, it solves it for ‘a’ first and then solves the resulting equation for ‘b’ in terms of an introduced variable ‘z’. That produces a multi-line warning in red (that I will not reproduce here), and the results:
a =
1 - 2*z
b =
z
that does not make sense to me. I consider this to be a bug, and I would prefer it to be an option rather than the default, but that is not my decision.
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Mech Princess on 20 Jul 2012
Sorry, one more issue regarding this. My variables alpha1, alpha2 and alpha3 are defined by sym and not syms. I need to do this as the no of alpha's is determined by the input data size. This case 3.
data = [-1 0 1;-1 +1 -1]'; alpha = sym('alpha',[1 3]); %output "[ alpha1, alpha2, alpha3]" st = 'alpha*data(:,2)=0' %output "alpha2 - alpha1 - alpha3 = 0" but I dont get this. instead, its something else v_2 = solve(st,alpha(1)) %doesnt work because the previous line is wrong
Do you have any suggestions for this? Thanks
Star Strider on 20 Jul 2012
This:
data = [-1 0 1;-1 +1 -1]';
alpha = sym('alpha',[1 3]);
advct = alpha * data(:,2)
v_2 = solve(advct == 0, alpha(1))
gives me these:
advct =
alpha2 - alpha1 - alpha3
v_2 =
alpha2 - alpha3
Is that the result you were hoping for?

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### More Answers (2)

Nitesh khanna on 1 Aug 2020
how to replace the variables a, b, c, d by variables w, x, y, z for; in eqn
eqn=a+b+c+d==9;
will this command work
eqn=subs(eqn, [a,b,c,d],[w,x,y,z])
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Bill Tubbs on 29 Jan 2023
As explained here by Paul, you can use the isolate function for this:
>> syms a b
>> eqn1 = b == (1 - a) / 2;
>> isolate(eqn1, a)
ans =
a == 1 - 2*b
>> isolate(eqn1, b)
ans =
b == 0.5000 - 0.5000*a
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Walter Roberson on 29 Jan 2023
.. Though mind you, that was not an option back in 2012 !
Star Strider on 29 Jan 2023
Definitely!
The isolate function was introduced in R2017a, 5 years after this thread.
I’ve used isolate extensively in my Answers since it was introduced, when its use was appropriate.

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