Asked by Omar
on 19 Oct 2013

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.

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Answer by sixwwwwww
on 20 Oct 2013

Edited by 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!

Answer by 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()

Answer by David
on 21 Oct 2013

Edited by 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().

Walter Roberson
on 21 Oct 2013

As long as anything in the equation is sym, the whole expression will be treated as sym. So

t = sym('t%d', [1 2]);

is enough to make the equations sufficiently sym() without requiring sym() around the equations.

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## 2 Comments

## Qasim Manzoor (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/90781#comment_175307

do you have to use a mathematical method or any way would be fine?

## Omar (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/90781#comment_175328

I don't know what you mean exactly. How would you solve this in a non-mathematical way?