I changed that, its still not working. Also, the values of the constants are not replaced in the expression for c[x].
Are you sure that you want to integrate on a null interval?
K = 1/((1/w)*Integrate[1/(\[Gamma]*c[x]), {x, -(w/2), -(w/2)}])
The function SolveValues outputs a list of list of rules. Triy this:
SolveValues
{{a1, a2, a3, a4, a5, a6}} = SolveValues[{eqn9, eqn4, eqn5, eqn6, eqn7, eqn8}, {A1, A2, A3, A4, C[2], C[1]}]