# Reduce does not solve a system of equations

Discussion in 'Mathematics' started by pau1996, Aug 2, 2020 at 2:25 AM.

1. ### pau1996Guest

I am trying to solve a system of 7 equations and 7 unknowns given a set of assuptions. I am only interested in obtaining V3 as a function of the exogenous parameters.

I am using the following code:

Reduce[V3 == (-12 s + 4 d V1 - 3 d l V1 + 4 d V2 - 3 d l V2 +
3 d l V4 + 2 d l V5 + 2 d l V6 + 2 d l V7 + 12 w1 + 12 w4)/(
12 - 4 d + 3 d l) &&
V2 == (-12 s + 4 d V1 - 3 d l V1 + 4 d V3 - 3 d l V3 + 3 d l V4 +
2 d l V5 + 2 d l V6 + 2 d l V7 + 12 w1 + 12 w3)/(
12 - 4 d + 3 d l) &&
V1 == (-12 s + 4 d V2 - 3 d l V2 + 4 d V3 - 3 d l V3 + 3 d l V4 +
2 d l V5 + 2 d l V6 + 2 d l V7 + 12 w1 + 12 w2)/(
12 - 4 d + 3 d l) &&
V4 == (12 s + d l V1 + d l V2 + d l V3 + 2 d l V5 + 2 d l V6 +
2 d l V7)/(3 (4 - 4 d + 3 d l)) &&
V5 == (-12 b + d l V1 + d l V2 + d l V3 + 3 d l V4 + 4 d V6 -
2 d l V6 + 4 d V7 - 2 d l V7 + 12 w2)/(2 (6 - 2 d + d l)) &&
V6 == (-12 b + d l V1 + d l V2 + d l V3 + 3 d l V4 + 4 d V5 -
2 d l V5 + 4 d V7 - 2 d l V7 + 12 w3)/(2 (6 - 2 d + d l)) &&
V7 == (-12 b + d l V1 + d l V2 + d l V3 + 3 d l V4 + 4 d V5 -
2 d l V5 + 4 d V6 - 2 d l V6 + 12 w4)/(2 (6 - 2 d + d l)) &&
w1 > s > w2 > w3 > w4 > b > 0 && w1 + w2 + w3 + w4 == 4 s &&
0 < d < 1 && 0 < l < 1, {V3, V2, V1, V4, V5, V6, V7, s}]

I solved similar systems using this method and I also tried to use Solve instead of Reduce without success. However, Mathematica does not return me anything in this case.

Does anyone know a different way to solve this problem?