HP Prime can't solve some nonlinear system of equations

[rombva]

The HP Prime G2 with last SW version can't solve these systems, but xCas solves it properly excluding example 2):

1) solve([x^2+y^2=a,1/x^2+1/y^2=b],[x,y])

G2 doesn't response while solving it.

2) solve([z^x=x,z^y=y,y^y=x],[x,y,z])

G2 returns a "Bad Argument Value" error.

3) solve([x^2-(y-z)^2=a,y^2-(z-x)^2=b,z^2-(x-y)^2=c],[x,y,z])

G2 returns an empty list []. The last beta emu unexpectedly closes after a few seconds.

4) solve([x^2+y^2=a*x*y*z,y^2+z^2=b*x*y*z,z^2+x^2=c*x*y*z],[x,y,z])

G2 returns only a [0 0 0]. The last beta emu unexpectedly closes after a few seconds.

5) solve([2*(x^2+y^2)=x*y*z,10*(y^2+z^2)=29*x*y*z,5*(z^2+x^2)=13*x*y*z],[x,y,z])

G2 returns an answer with variables x, y and z.

6) solve([4*x*y+x^2+y^2=1,8*x*z+x^2+4*z^2=-2,8*y*z+y^2+4*z^2=1],[x,y,z])

G2 returns an answer with variables x, y and z.

I discovered that while running some tasks the HP Prime's busy icon doesn't appears on the upper right corner of the screen.