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No Output Given : []

Hi all and thank you in advance for helping me. It shouldn't be a bad issue but when I try to find the solution to the following system of linear equations sage can't give me any solution, and gives the output "[ ]". The problem is that I have checked several times if I made something wrong on the formal aspect, but I don't find anything wrong (indeed sage doesn't tell me there is an error). I've set the system this way :

b, v, k, B, V, W, c, x, y, E, Q, H, S, P = var('b, v, k, B, V, W, c, x, y, E, Q, H, S, P')

eq1 = c(S+P)==(1-(y-x))(S)+(y-x)(S+PB)

eq2 = c(S+P)+(1-c)((2S+P)((V-c)/(1-c)))==(1-(y-x))((2S+P)(x/(1-(y-x))))+(y-x)(S+P*W)

eq3 = (2S+P)(x/(1-(y-x)))==S

eq4 = (S+P)k==S+PE

eq5 = (S+P)k+(1-k)((2S+P)((Q-k)/(1-k)))==S+P*H

eq6 = (2S+P)((b)/(1-(v-b)))==S

solve([eq1,eq2,eq3,eq4,eq5,eq6],b,v,k,c,x,y)

Output : []

I see that not all the operators will be visible, but anyway I've put them all, so that's not the problem. Do you have any idea about it? Thank you very much :)

No Output Given : []

b, v, k, B, V, W, c, x, y, E, Q, H, S, P = var('b, v, k, B, V, W, c, x, y, E, Q, H, S, P') P') eq1 = c(S+P)==(1-(y-x))(S)+(y-x)(S+PB) c*(S+P)==(1-(y-x))(S)+(y-x)(S+P*B) eq2 = c(S+P)+(1-c)((2S+P)((V-c)/(1-c)))==(1-(y-x))((2S+P)(x/(1-(y-x))))+(y-x)(S+P*W) c*(S+P)+(1-c)*((2*S+P)((V-c)/(1-c)))==(1-(y-x))((2*S+P)(x/(1-(y-x))))+(y-x)(S+P*W) eq3 = (2S+P)(x/(1-(y-x)))==S (2*S+P)*(x/(1-(y-x)))==S eq4 = (S+P)k==S+PE (S+P)*k==S+P*E eq5 = (S+P)k+(1-k)((2S+P)((Q-k)/(1-k)))==S+P*H (S+P)k+(1-k)((2*S+P)*((Q-k)/(1-k)))==S+P*H eq6 = (2S+P)((b)/(1-(v-b)))==S solve([eq1,eq2,eq3,eq4,eq5,eq6],b,v,k,c,x,y) (2*S+P)*((b)/(1-(v-b)))==S solve([eq1,eq2,eq3,eq4,eq5,eq6],b,v,k,c,x,y) Output : [][]

I see that not all the operators will be visible, but anyway I've put them all, so that's not the problem. Do you have any idea about it? Thank you very much :)