It is impossible to solve a system of equations with three variables with only two equations. you need three. Otherwise there are multiple solutions that could work.
You can look at the two equations as the equations of two planes. The intersection of those two planes form a line in 3D space. The solution(s) to the two equations would be any point on that line, but you would first have to find the equation of the line. That is the only way I know of finding values of x, y and z. There could be an infinite number of solutions, but each point (x,y,z) must fall on that line.