verify that the pair of functions x = t + e^t , y = te^t is a solution to the system of differential equations.

x + y - dy/dt = 1 , x - dx/dt = t - 1.

ok so i was able to prove that the pair of functions were solutions to the x + y - dy/dt = 1.

but i couldnt prove they were solutions to the equation on the right, x - dx/dt = t - 1.

any thoughts? thanks in advance.