Answer
$a.$
$\left\{\begin{aligned}
x-2z+2w&=5 \\
y+3z&=-1\\
z-w&=0\\
w&=-1\end{aligned}\right.$
$b.$
$(5,2,-1,-1)$
Work Step by Step
$a.$
$\left\{\begin{aligned}
x-2z+2w&=5 \\
y+3z&=-1\\
z-w&=0\\
w&=-1\end{aligned}\right.$
$b.$
The 4th equation gives $w=-1.$
Back-substituting $w=-1$ into the 3rd equation,
$z-(-1)=0\quad \Rightarrow\quad z=-1.$
Back-substituting into the 2nd equation,
$y+3(-1)=-1\quad \Rightarrow\quad y=2.$
Back-substituting into the 1st equation,
$x-2(-1)+2(-1)=5\quad \Rightarrow\quad x=5.$
The solution is $(5,2,-1,-1)$.
