How to solve equations having product variables

I have 3 equations.

• x+y+z=2
• x+3y+4z=7
• x-2y+3z+xy+yz+zy+xyz=6

When I search, many people use the "A\b" function, how should I write it in my case?

A = [ 1 1 1 0 0 0 0 0 ; 1 3 4 0 0 0 0 0; 1 -2 3 1 1 1 1 ];
b = [ 2; 7; 6];

I want to get value of x, y, z.

The above code is not correct, but I want to write it like that.

What function should be used to solve it?

Answer 1

[Manan Mishra]

You can use the function fsolve to solve a system of non-linear equations.

Please refer the following link to know more about this function:

https://www.mathworks.com/help/optim/ug/fsolve.html

You can also refer the examples in the above link for a better understanding of the function.

The following steps might help you:

1. Convert the equations to the form F(x) = 0.

2. Write a function that computes the left-hand side of these three equations.

3. Save this code as a file on your MATLAB path.

4. Solve the system of equations starting at the given point.

function f = eqn(x)

f(1) = x(1)+x(2)+x(3)-2;
f(2) = x(1)+3*x(2)+4*x(3)-7;
f(3) = x(1)-2*x(2)+3*x(3)+x(1)*x(2)+x(2)*x(3)+x(3)*x(1)+x(1)*x(2)*x(3)-6;

end

Save this function as a file and execute the following code.

func = @eqn;
x0 = [0,0,0];
x = fsolve(func,x0)