Today I tried to plot a plane by using its coordinate form:
plot 3x+3y-2z=18
that worked pretty good and gave me the following result:
http://www.wolframalpha.com/share/clip?f=d41d8cd98f00b204e9800998ecf8427enonbipn9a6
However I want to include another two planes into that surface plot by using:
plot 3x+3y-2z=18, 1x+3y-2z=5, 0x-6y+4z=3
In Mathematica, you would use the ContourPlot3D function for this ContourPlot3D: Create a 3D contour plot of a function—Wolfram Documentation
It may not be possible to create a 3D plot with multiple contours yet in Wolfram|Alpha, but I haven’t been able to do it yet.
Wolfram|Alpha doesn’t have a defined syntax, so there isn’t anything generally wrong with your input.
Thanks for your quick reply Sean.
It’s a real pitty that Wolfram|Alpha does not support plotting multiple planes. So the only option left is to buy mathematica? 
With regards,
Jan
Jan gave very good advice. For multiple planes in one graph, Show[graphics,options] would also be needed. E.g.:
Show[ContourPlot3D[x == 2, {x, -5, 5}, {y, -5, 5}, {z, -5, 5}],
ContourPlot3D[y == 3, {x, -5, 5}, {y, -5, 5}, {z, -5, 5}],
ContourPlot3D[z == 4, {x, -5, 5}, {y, -5, 5}, {z, -5, 5}]]
You can plot two planes (but no more than two) in Wolfram|Alpha, by doing something like this:
plot (3x+3y-2z-18)(x+3y-2z-5)=0
Also try:
plot (x+y+z-10)(x+y/10+z-5)=0