For this code
R = PolynomialRing(QQ, 'x', 2)
X = vector(R.gens())
show(X)
A=matrix(QQ,[[1, 2], [-3, 4]])
b=vector(QQ,[[2], [-4]])
show(A,"....", b)
Z=A*X+b
ZZ=[SR(y) for y in Z]
ZZZ=[eq<=0 for eq in ZZ]
Y=[SR(X[i]).variables()[0] for i in range(len(X))]
show(Y)
show(ZZZ)
sol=solve_ineq(ZZZ,[x[0]])
sol
sol[0]
gives [x0 == -2*x1 - 2, 5*x1 + 1]
. And here is the question what means 5*x1 + 1
(no equality, inequality ...)