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System of equations solver/ xy+xz+zy=1; xy(x+y)+yz(y+z)+xz(x+z)=48; xy(x^2+y^2)+yz(y^2+z^2)+xz(x^2+z^2)=118

xy+xz+zy=1; xy(x+y)+yz(y+z)+xz(x+z)=48; xy(x^2+y^2)+yz(y^2+z^2)+xz(x^2+z^2)=118

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x*y + x*z + z*y = 1
$$y z + \left(x y + x z\right) = 1$$ 
x*y*(x + y) + y*z*(y + z) + x*z*(x + z) = 48
$$x z \left(x + z\right) + \left(x y \left(x + y\right) + y z \left(y + z\right)\right) = 48$$ 
    / 2    2\       / 2    2\       / 2    2\      
x*y*\x  + y / + y*z*\y  + z / + x*z*\x  + z / = 118
$$x z \left(x^{2} + z^{2}\right) + \left(x y \left(x^{2} + y^{2}\right) + y z \left(y^{2} + z^{2}\right)\right) = 118$$ 
(x*z)*(x^2 + z^2) + (x*y)*(x^2 + y^2) + (y*z)*(y^2 + z^2) = 118
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