I have three equations with three unknown variables. The form of the equation is:

c1*x + c2*y + c3*z = 0

c4*x + c5*y + c6*z = 0

c7*x + c8*y + c9*z = 0

All three equations are equal to zero. The constants are known.

Is there a simple and general way to find the values for x,y and z without all the variables being zero?

Thank you.