# What is the name of these equations?

$xy=0$

$ax +by +cxy +d=0$

$ax +by +cz +dxy +eyz +gxyz=0$

I made myself the examples, sometimes I face these equations and I do not know how to resolve them, all equations whose unknowns have exponent equals one but they can be multiplied together as I have put in the example $xy$, $yxzt$.... I want to know the name so I can find info and understand them because I google equations and many different come, mostly linear but I do not see these ones. I did not see the tag "equations" so I tagged differential-equations but I do not think It is that.

• I suppose the term for such equations would be "systems of multilinear equations". Jan 17, 2012 at 14:03

In terms of nomenclature, equations of the form $$c_1 x_1 + c_2 x_2 + \ldots$$
where $c$ is a constant are known as linear equations, equations: $$c_1 x_1 x_2 + c_2 x_2 x_3 + \ldots$$
are bilinear equations. Though not as common, equations of the form: $$c_1 x_1 x_2 x_3 + c_2 x_2 x_3 x_4 + \ldots$$ are referred to as trilinear equations. For higher orders @Raskolnikov suggested "systems of multilinear equations". Also, see the comment by @Lieven below who calls them "multilinear equations in homogeneous space".