# Convert system of quadratic equations into system of linear equations

Let's say that I have a system of N quadratic equations in the form: $(\alpha x+\beta y+\gamma z)^2=k$ and I want to convert it to equations of the form $\alpha' a +\beta' b + \gamma' c+...=k$ such that $a=x^2$, $b=xy$, $c=xz$... and so on. I know how to do this by hand, but I have too many equations for that. I believe there is an easy and clean way to do this in Mathematica but I can't figure out how.

Thanks.

• apply CoefficientList for both left- and right-hand side of the equation? – egwene sedai Feb 21 '18 at 17:34
• I think that CoefficientList will be me the coefficients next to the variables. I want a list with the variables, in the form ${x^2,xy,xz,y^2,...}$ and then I would like to change those variables in the equations for ${a,b,c,d,e,...}$ – Psyphy Feb 21 '18 at 17:58