# How would I write a code to solve a system of equations?

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Omar on 19 Oct 2013
Answered: anjali wavhale on 1 Dec 2020
I need to solve a system of equations but I do not know the syntax for doing so. The equations are:
q1 = (1.53*10^-5)*t1^4 + (1.67*10^-2)*t1^3 + 6.85*t1^2 + 2746*t1 - 57793
q2 = 13.3*(t1-t2)
q3 = (1.53*10^-5)*t2^4 + (1.67*10^-2)*t2^3 + 6.85*t2^2 + 4846*t2 - 49161
also; q1=q2=q3
I'm new to MATLAB and not sure how to handle this many variables along with the scientific notation.
##### 2 CommentsShowHide 1 older comment
Omar on 20 Oct 2013
I don't know what you mean exactly. How would you solve this in a non-mathematical way?

sixwwwwww on 20 Oct 2013
Edited: sixwwwwww on 20 Oct 2013
Dear Omar, you can solve your system of equations using the following way:
t = sym('t%d', [1 2]);
q1 = 1.53e-5 * t(1)^4 + 1.67e-2 * t(1)^3 + 6.85 * t(1)^2 + 2746 * t(1) - 57793;
q2 = 13.3 * (t(1) - t(2));
q3 = 1.53e-5 * t(2)^4 + 1.67e-2 * t(2)^3 + 6.85 * t(2)^2 + 4846 * t(2) - 49161;
[solutions_t1, solutions_t2] = solve(q1 == q2 == q3, t(1), t(2))
Or
[solutions_t1, solutions_t2] = solve(q1 == q2, q2 == q3, t(1), t(2))
You can check which solutions are better because in first case you will get 4 solutions for both t1 and t2 and in second case you will get 16 solutions for both t1 and t2. I hope it helps. Good luck!
sixwwwwww on 20 Oct 2013
You are welcome dear

Walter Roberson on 20 Oct 2013
{q = 2003.839045, t1 = -819.5264017, t2 = -970.1909915},
{q = -10982.94224, t1 = -817.9943073, t2 = 7.790823431},
{q = 133.2164095, t1 = 20.04280634, t2 = 10.02653495},
{q = 13235.45859, t1 = 24.30348638, t2 = -970.8437757}
provided that you only want real-valued solutions.
This was done by substituting t1 for t(1) and t2 for t(2), and then plugging the three q equations into solve()

David on 21 Oct 2013
Edited: David on 21 Oct 2013
In addition to the answers already posted, be sure to put sym() around each of your equations. That is to say, do the following:
syms t1 t2
q1 = sym( 1.53e-5*t(1)^4 + 1.67e-2*t(1)^3 + 6.85*t(1)^2 + 2746*t(1) - 57793 );
q2 = sym( 13.3*(t(1) - t(2)) );
q3 = sym( 1.53e-5*t(2)^4 + 1.67e-2*t(2)^3 + 6.85*t(2)^2 + 4846*t(2) - 49161 );
[solutions_t1, solutions_t2] = solve(q1 == q2, q2 == q3, t1, t2);
solve requires that your equations be symbolic objects which is guaranteed by using sym().
##### 2 CommentsShowHide 1 older comment
David on 22 Oct 2013
Oh? This seemed to correct a problem I was having earlier in using the solve function. You actually saw that question and made useful suggestions, though suggestions that did not quite do the trick. Maybe we are both missing something or maybe it's just me...

anjali wavhale on 1 Dec 2020
how to do least square estimation for system with the prbs as input to it

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