Answer
$a.$
$\left\{ \begin{aligned}
x+2y+3z-w&=7\\
y-z&=5\\
z+2w&=5\\
w&=3\end{aligned}\right.$
$b.$
$(7,3,-1,3)$
Work Step by Step
$a.$
$\left\{ \begin{aligned}
x+2y+3z-w&=7\\
y-z&=5\\
z+2w&=5\\
w&=3\end{aligned}\right.$
$b.$
The 4th equation gives $w=3$.
Back-substituting $w=3$ into the 3rd equation,
$z+2(3)=5\quad \Rightarrow\quad z=-1.$
Back-substituting $w=3$ and $z=-1$ into the 2nd equation,
$y-2(-1)=5\quad \Rightarrow\quad y=3.$
Back-substituting into the 1st equation,
$x+2(3)+3(-1)-(3)=7\quad \Rightarrow\quad x=7.$
The solution is $(7,3,-1,3)$
