Solving systems by substitution classwork – solve each of the following systems by substitution. x = 4y – 9 x = y + 3 5x = -2y + 48 x = -3y + 20 y – 4x = 28 y = -2x – 2 y + 2x = -12 y = x + 15 x = -2y – 7 2x + y = -14

Let x have probability generating function gx (s) and let un generating function u(s) of the sequence uo, u1, satisfies p(x > n). show that the (1- s)u(s) = 1 - gx(s), whenever the series defining these generating functions converge.