I'm having a trouble solving a system of equations with multiple parameters and unknowns
syms a b c k t p1 p2 v1 v2 x
eqn_x = x == a + ((p2-v2)-(p1-v1))/(2*t*(1-a-b)) + (1-a-b)/2 ;
eqn_p1 = p1 == c - k + (1/3)*(v1-v2) + t*(1-a-b)*(1+(a-b-4*v1-2*v2)/3) ;
eqn_p2 = p2 == c - k + (1/3)*(v2-v1) + t*(1-a-b)*(1+(a-b-4*v2-2*v1)/3) ;
eqn_v1 = v1 == (c - k + (1/3)*t*(1-a-b)*(3+a-b) + t*(2*(x-a)^2 - (1-b-x)^2))/(1+2*t*(1-a-b)) ;
eqn_v2 = v2 == (c - k + (1/3)*t*(1-a-b)*(3+b-a) + t*(2*(1-b-x)^2 - (x-a)^2))/(1+2*t*(1-a-b)) ;
eqns = [eqn_x, eqn_p1, eqn_p2, eqn_v1, eqn_v2] ;
S = solve(eqns, [p1 p2 v1 v2 x]) ;
This is my code, the goal is to get v1 and v2 term rearranged in terms of only a, b, c, k, & t terms.
there are 5 functions and 5 unknowns. though it is not a system of linear equation because v1 and v2 term depends on quadratic function of x, I guess there is a possible rearrangement.
But what I get is p1, p2, v1, v2, x being [0x1 sym]. How do I get those rearrangement?