Answer
$a. $
$\left\{\begin{array}{l}
x+2y+3z-w=7\\
y-2z=5\\
z+2w=5\\
w=3
\end{array}\right.$
$b.$
$(7,3,-1,3)$
Work Step by Step
$a. $
$\left\{\begin{array}{l}
x+2y+3z-w=7\\
y-2z=5\\
z+2w=5\\
w=3
\end{array}\right.$
$b.$
Back substitute $w=3 $ into
$z+2w=5$
$z+2(3)=5$
$z+6=5$
$z=-1$
Back substitute $z=-1 $ into
$y-2z=5$
$y-2(-1)=5$
$y+2=5$
$y=3$
Back substitute $y=3, z=-1,w=3 $ into
$x+2y+3z-w=7$
$x+2(3)+3(-1)-3=7$
$x+6-3-3=7$
$x=7$
Solution: $(7,3,-1,3)$
