#### Answer

Equation $2$ does not contain the variable z. To obtain a second equation that does not contain this variable, we can add equations $1$ and $3$.

#### Work Step by Step

The provided system of equations is as follows;
$x+y+z=2$ (I)
$2x-3y=3$ (II)
$10y-z=12$ (III)
It is clear from equation (II) that it does not contain the variable z.
In order to get the equation that does not contain z, simply add equations (I) and (III) to get;
$\begin{align}
& x+y+z+10y-z=2+12 \\
& x+11y=14
\end{align}$
Thus, the above equation contains only the variable x and y but does not contain z.