Can somebody please help me explain why the following system of equations (with variables a, b, c, d and e):

$\displaystyle 20a + 16c + 4e = 2300$

$\displaystyle 200b + 152c + 20d + 28e = -2300$

$\displaystyle 16a + 152b + 168c = 1800$

$\displaystyle 20b + 20d = -700$

$\displaystyle 4a + 28b + 32e = 500$

has no solutions? I'll put it into an augmented matrix to make it easier for you (if that helps):

$\displaystyle \begin{bmatrix}

20 & 0 & 16 & 0 & 4 & 2300 \\

0 & 200 & 152 & 20 & 28 & -2300 \\

16 & 152 & 168 & 0 & 0 & 1800 \\

0 & 20 & 0 & 20 & 0 & -700 \\

4 & 28 & 0 & 0 & 32 & 500

\end{bmatrix}$

I seem to be having trouble explaining this so if you could help me out, that would be greatly appreciated.

Thanks.