Solve 4 equations with 4 unknowns

[EssoExplJoe]

I am trying to solve for 4 unknowns in 4 equations as below. I have managed to write a VBA routine to solve for 3 unknowns with 4 equations but I am getting totally lost in the weeds trying with 4 unknowns (4 cubic equations). Does any have any VBA routines that does this?

Points: (Y₁,X₁), (Y₂,X₂), (Y₃,X₃), (Y₄,X₄)
Points: (10,2), (5,4), (4,11), (4,15)
Four Equations with 4 variables:
a) Y₁=a+bX₁+cX₁²+dX₁³
b) Y₂=a+bX₂+cX₂²+dX₂³
c) Y₃=a+bX₃+cX₃²+dX₃³
d) Y₄=a+bX₄+cX₄²+dX₄³
Solve for a,b c and d :

 

[StephenCrump]

Solver got pretty close, although I don't know if the results are meaningful:

Excel 2010
	A	B	C
1	Variable	Value	Result
2	a	-0.10768262	10.0000001
3	b	1.92719490	0.0000000
4	c	94.58702592	0.0000000
5	d	4.03616127	0.0000000
Sheet1

 

[StephenCrump]

Sorry for any confusion (your PM) ...

- "Value" is the solved value for each variable, e.g. a is solved as -0.10768262

- Result is the value of each of your four equations using the solved values, e.g.
-A*B^2 + C*B^-3 + B/5 - 4 (using a = -0.10768262 etc) = 10.0000001 (very close to the 10 you require).