Help needed! 3 Simultaneous Equations, 2 Variables

I have 3 equations with two variables (x,y) to find. and the equations contain (x^2,y^2,x,y,xy)

can matlab solve this type of equation?

the matlab code that i used:

[x,y] = solve('2*(x^2)+y^2+0.1*x+0.41','0.4*(x^2)-0.11*(y^2)+3*x-0.1*y+0.34*x*y+0.16','0.3*(x^2)+0.4*(y^2)-0.5*y-0.8');

but it failed and the warnings i get are:

Warning: 3 equations in 2 variables. Warning: Explicit solution could not be found.

anyone knows if there is other solution to find the x and y? Thanks. I'm new to MATLAB and hope someone will point out the error.

[David]

Well I think your problem is that your system is over determined. That is there are too many constraints on the system. No values of x and y will satisfy all three equations unless some kind of miracle happens.

Try just using two equations and I bet you will find that a solution is returned.

Answer 1

[Walter Roberson]

Those three equations are not consistent in two variables.

If you solve() the first two as a pair, and then solve() the first and third, you can see that the answers are quite different.

What kind of answer were you hoping for?

[sy]

hi Walter,

I simply put some constants as the coefficients just to illustrate what type equations that I have.

This is the equation that i actually want to solve:

(4*(s^2)-4*(del1^2))*(x^2)-4*(del1^2)*(y^2)+(4*s*(del1^2)-4*(s^3))*x+(del1^4)+s^4-4*(d^2)*(del1^2)-2*(s^2)*(del1^2);

and two other equation, s,d,del1 are constants that are dependent on the condition.

I derived the equations myself (hope they are not wrong) to find the position of a beacon signal source relative to four receivers. del1 is the difference between distance travelled by signal to reach receiver 1 and 4. x, and y are the coordinate (that i wish to find from the equations)