I have 4 equations with 4 unknowns. The equations, however, are not of the simple form: $$aw + bx + cy + dz = 0$$ They contain complex combinations of the variables and approximately 10-15 terms.
Examples:
eq1: $$-156 wx^2 z^2 + 111.28 x^2 z^2 -333.84w^2z^2+176.7wz^2+446.64wx^2-13.76wx^2y+156wx^2y^2-536.85x^2+58.44x^2y+111.28x^2y^2-254.77z^2 = 0 $$
eq 2:$$156w^2x^2z^2-222.56wx^2z^2-146.6x^2z^2+445.12w^3z^2-353.36w^2z^2-446.64w^2x^2+13.76w^2x^2y-156w^2x^2y^2+1018.08wz^2+1073.7wx^2-116.88wx^2y-222.56wx^2y^2-803.78x^2+55.66x^2y-146.6x^2y^2 = 0 $$
eq 3:$$6.88x^2z^2-156.x^2yz^2-6.88w^2z^2+156w^2yz^2+58.44wz^2+222.56wyz^2-27.33z^2+146.6yz^2-31.77x^2+446.64x^2y-20.64x^2y^2 = 0$$
eq 4:$$446.64x^2z^2-13.76x^2yz^2+156x^2y^2z^2-446.64w^2z^2+13.76w^2yz^2-156w^2y^2z^2+1073.7wz^2-170.88wyz^2-222.56wy^2z^2-803.78z^2+54.66yz^2-146.6y^2z^2+127.08x^2y-893,28x^2y^2+27.52x^2y^3 = 0$$
Where I need to solve for $w$, $x$, $y$ and $z$.
The real equations are much longer, and more complex with many more variations
- Can I solve this simultaneously?
- Is there any easier way of solving this?
- Is it possible to solve this at all?
I have attempted to use the Newton-Raphson method to solve this, but I did not understand a lot of what I was required to do. Hope the actual equations help.
Thank You.
There is no unique solution. For $x=w=0$ any $y$ and $z$ are ok. Or if $x=z=0$ the system of equations is solved for any $y$ and $w$