Is there a way I can figure out what values of the coefficients of some system of non-linear equations makes the system inconsistent? Take the following system of equations as an example. The unknowns are (y_0,..., y_8) I do not have fixed values for the coefficients a,b,c,d,e,f,g,h,u,v,w so I just want to know which values of a,b,c,d,e,f,g,h,u,v,w make the system inconsistent. Note that in the example I am using the system is underdetermined as I have 9 unknowns and only 8 equations. In the linear system case, I know that if one has the same number of unknowns as the number of equations then the solvability boils down to computing the determinate of the coefficient matrix. How about the non-linear underdetermined system case?

uy_5 + ey_7 - e + by_2y_0 + cy_2 + wy_0 =0

dy_5 + fy_7 - f + ay_2 + vy_0 = 0

uy_6 - wy_7 + by_3y_0 + by_2y_1 + cy_3 + wy_1 = 0

uy_8 - cy_7 + by_4y_0 + c*y_4 =0

dy_8 - ay_7 + a*y_4 = 0

dy_6 - vy_7 + ay_3 + vy_1 = 0

by_7 - by_4*y_1 = 0

y_1 = 0

Any hints or help would be highly appreciated.

Many Thanks