How to solve simultaneous equation with identity

I have a set of simultaneous equations which I can't figure out how to solve properly. I have to do it simultaneously, but also follow an identity as x^2 + y^2 + z^2 =1 to yield any solution other than 0 for each variable. I've tried to use symbolic functions but that I can't figure out. How can I set up a script for finding the answers to this type of system of equations?

[A1x + A2y + A3z;

B1x + B2y + B3z;

C1x + C2y + C3z;

x^2 + y^2 + z^2]

=

[0;

0;

0;

1]

I'm not good at formatting.

Answer 1

[KALYAN ACHARJYA]

https://in.mathworks.com/help/symbolic/solve-a-system-of-linear-equations.html

[Trygve Pollen]

It is a non-linear simultaneous equation that has to adhere to the identity. I've tried to use solve() by splitting the equations line by line using their symbolic variables. However I get the 'empty sym 0-by-1' output for the solution. I think the method is correct, but the solutions for x,y,z need to be approximated. Is there a way to make the solution an approximate if it turns out that 0.000001x + y =1 to yield y=1 for instance?