We can write the system as
\(\begin{pmatrix} 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 1 \\ 1 & 0 & 1 & 1 \\ 0 & 1 & 1 & 1 \end{pmatrix} \begin{pmatrix} w \\ x \\ y \\ z \end{pmatrix} = \begin{pmatrix} -2 \\ 4 \\ 19 \\ 12 \end{pmatrix}\)
The solution is then (w,x,y,z) = (-3,-7,8,14), so wx + yz = (-3)(-7) + (8)(14) = 133.
+1694 w + x + y = - 2
________________
w + y + z = 19
x + y + z = 12
--------- w = x + 7 (1)
w + x + z = 4
w + y + z = 19
--------- y = x + 15 (2)
_________________
w + x + y = - 2
x = - 2 - w - y
x = - 2 - (x + 7) - (x + 15)
x = - 8
w = - 1
y = 7
z = 13
---------------------
wx + yz = (- 1)(- 8) + 7(13) = 99
