Robert's response is correct, but if you are a newcomer to Maple, you may not know how to enter "your equations". Here is an excerpt from a Maple 11 worksheet showing a few ways to approach your problem:

The first step is to define the three equations (note the use of * for multiplicaiton and := for assignment):

eq1 := 3*x+2*y+z=2;
                              3 x + 2 y + z = 2
eq2 := 4*x+2*y+2*z=8;
                             4 x + 2 y + 2 z = 8
eq3 := x-y+z=4;
                                x - y + z = 4

Here is what Robert's solution would look like:

solve( {eq1,eq2,eq3} );
                           {y = 2, x = -4, z = 10}

It is exactly the same as you would see if you explicitly entered the unknowns as a set:

solve( {eq1,eq2,eq3}, {x,y,z} );
                           {y = 2, x = -4, z = 10}

If you specify the unknowns as a list (which has order), the output is slightly different:

solve( {eq1,eq2,eq3}, [x,y,z] );
                          [[x = -4, y = 2, z = 10]]

I hope this is helpful,

Doug

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Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/