Question: difficulty solving equations over reals

I would like to solve {x^2+y^2+z^2 = 3, x+y+z = 3} over the reals. Clearly x=1,y=1,z=1 is a solution.

Maple seems to have a hard time with this. I have tried using with(RealDomain) and various commands.

The last solution  is getting closer to the real number answer if i substitute z = 1, but then i get the strange answer { 1=1, x=1,y=1}

I tried using wolfram and it showed me the correct answer.

Rest assured, I am a strong maple fan. I sometimes use wolfram for quick and dirty solutions.

Also is there a way to turn off "with(RealDomain)", switch back to the default domain, without using 'restart'. 

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