Solve the system of equations? What is this format of an answer? So I solved this system without using matrices, just by (sort of) reverting to high school math instincts.
$$w+x=-5$$
$$x+y=4$$
$$y+z=1$$
$$w+z=8$$
From this, I got $w=-9,x=4,y=0$ and $z=1$. How would I convert this back to what appears to be a matrix form?
From the format, you get that $x_i=a_i+s*b_i$

$x_1+x_2=-5 =&gt; a_1+a_2+s(b_1+b_2) = -5$ for all s. Thus, $b_1=-b_2$

Similarly, you get $b_1=-b_2=b_3=-b_4$ 

The solution you got is for $a_1, a_2,a_3,a_4$

Thus, 
$x_1 = -9+s*1$ (taking $b$ into $s$)

$x_2=4+s*(-1)$

$x_3=0+s*(1)$

$x_4=1+s*(-1)$
i guess that answers your question