Example 6. Through the line with the general equations

$$
\left\{\begin{array}{l}
3 x-2 y+5 z+3=0 \\
x+2 y-3 z-11=0
\end{array}\right.
$$

and the origin, draw a plane and derive its equation.
Solution. We reduce the problem to constructing a plane through three points ( $\$ 1$, p. $4^{\circ}$ ). Substitute $z=-2$ into the original system and solve it for $x, y$. We get one point $M_{1}(3,1,-2)$ on the given line. To find another point on this line, we set $z=6: M_{2}(-1,15,6)$. It remains to 
compose the equation of the plane through three points: $\left|\begin{array}{ccc}x & y & z \\ 3 & 1 & -2 \\ -1 & 15 & 6\end{array}\right|=0$, i.e., $18 x-8 y+23 z=0$.