Simple eigenvalue problem (x'=[2x2]x)

Hi, I've got a homework problem that should be very simple, the previous problem was identical (different numbers) and was a breeze, but this one is giving me problems. Here's what we're asked for:
Apply the eigenvalue method to find the particular solution to the system of differential equations
$x'=\begin{bmatrix} 4 & 4\\ 3 & 5 \end{bmatrix}x$
which satifies the initial conditions
$x(0)=\begin{bmatrix} -4\\ 2 \end{bmatrix}$

So I begin by finding the eigenvalues from the characteristic equation:
$(4-\lambda)(5-\lambda)-12=(\lambda^2-9\lambda+8)=(\lambda-1)(\lambda-8)$
$\lambda=1,8$
To get the matrices:
$\begin{bmatrix} 3 & 4\\ 3 & 4 \end{bmatrix}\begin{bmatrix} a\\ b \end{bmatrix}=0$
and
$\begin{bmatrix} -4 & 4\\ 3 & -3 \end{bmatrix}\begin{bmatrix} a\\ b \end{bmatrix}=0$
To get
$\begin{bmatrix} a\\ b \end{bmatrix}=\begin{bmatrix} -4\\ 3 \end{bmatrix}$ and $\begin{bmatrix} a\\ b \end{bmatrix}=\begin{bmatrix} 1\\ 1 \end{bmatrix}$

Which gives the particular solution $x_p=a\begin{bmatrix} -4\\ 3 \end{bmatrix}e^t+b\begin{bmatrix} 1\\ 1 \end{bmatrix}e^{8t}$

But at this point, no values for a and/or b will satisfy $x(0)=\begin{bmatrix} -4\\ 2 \end{bmatrix}$

Can anyone help me out, please?
Thanks!