Relative position of plane and plane
A distinction is made between three possible relative positions between two planes $E$ and $F$.
 They intersect.
 They are parallel.
 They are coincident.
Remember
Similar to the relative position of a line and a plane, one tries to calculate the intersection line.
However, if you come across a true statement (e.g. 0 = 0), the planes are coincident. If the statement is incorrect (e.g. 8 = 0), they are parallel.
Hint
Example
$\text{E: } xy+z=2$
$\text{F: } 2x+y+z=4$

Set up a system of equations
The two equations can be viewed as a system of equations. $xy+z=2$
 $2x+y+z=4$
Now you should eliminate a variable. This is achieved here, for example, by adding the two equations.
I.+II.
$3x+2z=6$

Replace variable with $r$
One of the other variables is now replaced by $r$ and inserted in the equation. For example x:$\color{red}{x=r}$
$3r+2z=6$
The other variable ($z$) can now be expressed as a function of $r$. Simply solve equation for $z$.
$3r+2z=6\quad3r$
$2z=63r\quad:2$
$\color{red}{z=31.5r}$One of the two plane equations can also be used to determine $y$ by using $x$ and $z$.
$xy+z=2$
$ry+(31.5r)=2$
$0.5ry+3=2\quad+y$
$0.5r+3=2+y\quad2$
$\color{red}{y=0.5r+1}$ 
Set up equation of a line
First we write the results for $x$, $y$ and $z$ among themselves. $x=r$
 $y=0.5r+1$
 $z=31.5r$
Sorted:
 $x=\color{blue}{0}\color{green}{+1}r$
 $y=\color{blue}{1}\color{green}{0.5}r$
 $z=\color{blue}{3}\color{green}{1.5}r$
This can now be easily put into the form of a equation of a line.
$\vec{x} = \begin{pmatrix} \, \\ \, \\ \, \end{pmatrix} + r \cdot \begin{pmatrix} \, \\ \, \\ \, \end{pmatrix}$
$\vec{x} = \begin{pmatrix} \color{blue}{0} \\ \color{blue}{1} \\ \color{blue}{3} \end{pmatrix} + r \cdot \begin{pmatrix} \color{green}{1} \\ \color{green}{0.5} \\ \color{green}{1.5} \end{pmatrix}$
Example (parallel)
$\text{E: } xy+z=2$
$\text{F: } 2x2y+2z=7$

Set up a system of equations
 $xy+z=2\,\,\,\cdot(2)$
 $2x2y+2z=7$
We apply the addition method.
 $2x+2y2z=4$
 $2x2y+2z=7$
I.+II.
$0=3$ f. s. 
Interpret the result
We obtain a contradiction or a false statement.$0\neq3$
$E$ and $F$ therefore have no common point. The planes must be parallel.
=> $E$ and $F$ are parallel