identify three variables

x-y=1

y-2z=1

3x-4z=7

x=?

y=?

z=?

$\begin{array}{lrcll} (1) & x-y&=&1 \\ & x &=& 1+y \\ \hline (2) & y-2z&=&1 \\ & y &=& 1+2z \\ \hline (3) & 3x-4z&=&7\\ & 3x &=& 7 + 4z &\qquad x = 1+y\\ & 3(1+y) &=& 7 + 4z &\qquad y = 1+2z \\ & 3[1+(1+2z)] &=& 7 + 4z \\ & 3(1+1+2z) &=& 7 + 4z \\ & 3(2+2z) &=& 7 + 4z \\ & 6+6z &=& 7 + 4z \qquad &| \qquad -4z \\ & 6+6z-4z &=& 7 \\ & 6 + 2z &=& 7 \qquad &| \qquad -6 \\ & 2z &=& 7 -6\\ & 2z &=& 1 \qquad &| \qquad :2 \\ & \mathbf{z} &\mathbf{=}& \mathbf{0.5}\\ \hline (2) & y &=& 1+2z \\ & y &=& 1+2(0.5)\\ & y &=& 1+1\\ & \mathbf{y} &\mathbf{=}& \mathbf{2}\\ \hline (1) & x &=& 1+y \\ & x &=& 1+2\\ & \mathbf{x} &\mathbf{=}& \mathbf{3} \end{array}$