Answer
$\left\{\begin{array}{lllll}
x & -y & & +w & =-1\\
x & +y & +2z & +4w & =2
\end{array}\right.$
Work Step by Step
The product of the two matrices on the LHS is a 2$\times$1 matrix:
$\left[\begin{array}{l}
x-y+0z+w\\
x+y+2z+4w
\end{array}\right].\qquad $Equating it to $\left[\begin{array}{l}
-1\\
2
\end{array}\right]$ leads to
the system of equations
$\left\{\begin{array}{lllll}
x & -y & & +w & =-1\\
x & +y & +2z & +4w & =2
\end{array}\right.$
