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For the first solve question, you need to specify that you are solving for x and y.

solve([2*x+y==0,x-2*y==1],[x,y])

For the second question, you can do the following:

var('x y')
assume(x,'real')
assume(y,'real')
z=x+i*y
f=5*z-i*conjugate(z)^2+3+2*i
solve([f.real(),f.imag()],[x,y])