Final answer:
To solve the given system of simultaneous equations, we can use algebraic methods such as substitution or elimination, involving many steps that need to be carefully verified to find the values of x, y, and z.
Step-by-step explanation:
To solve the simultaneous equations for the unknowns x, y, and z, we will use methods such as substitution or elimination. The system of equations given is:
- -2x + 3y - 6z = 0
- 7x + 4y - 6z = -6
- 9x - 2y + 6z = -6
We will first simplify the equations if possible and then either eliminate one variable at a time or substitute after solving one equation for a variable. This process entails many algebraic steps which require careful checking and rechecking to ensure the solution is accurate. For example, one can start by adding the first and third equations to eliminate z, and then isolate y in the second equation to substitute into the modified first equation. After finding one variable, we back-substitute to find the others.