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Let Sage solve a system of equations:

sage: a,b,c,d,z = var('a,b,c,d,z')
sage: eqn1= a * d == b + a * (1-d)
sage: eqn2 = z == d / (1 - d)
sage: S = solve([eqn1,eqn2], d,z);  S

[ [d == 1/2*(a + b)/a, z == (a + b)/(a - b)] ]