Each equation is from 2nd degree and represent relation of two of them.
Let the three equations be fi(x1,x2,x3,x4) = ci or fi(x1,x2,x3,x4) - ci =0 , for all i =1,2,3
then d1* (f1(x1,x2,x3,x4) - c1) + d2*(f2(x1,x2,x3,x4) - c2) + d3*(f3(x1,x2,x3,x4) - c3)=0 represents the individual equations for (d1,d2,d3): (1,0,0), (0,1,0), (0,0,1) respectively.
Assume that given equations are of the forms f1(x1, x2, x3, x4) = 0,
f2(x1, x2, x3, x4) = 0 and f3(x1, x2, x3, x4) = 0. If f1, f2 and f3 are real functions of four real variables x1, x2, x3, x4, then the previously system of three equations is equivalent with the following equation:
(f1(x1, x2, x3, x4))2 + (f2(x1, x2, x3, x4))2 + (f3(x1, x2, x3, x4))2 = 0.
Moreover, if f1, f2 and f3 are complex functions of four complex variables z1, z2, z3, z4, then the system f1(z1, z2, z3, z4) = 0, f2(z1, z2, z3, z4) = 0, f3(z1, z2, z3, z4) = 0 is equivalent with following equation:
|f1(z1, z2, z3, z4)| + |f2(z1, z2, z3, z4)| + |f3(z1, z2, z3, z4)| = 0.
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