302

a)
$\begin{cases} x+y+2z=7&\left(1\right)\\ -x-y+z=2&\left(2\right)\\ 2x+y+z=6&\left(3\right) \end{cases}$
$+\begin{cases} x+y+2z=7&\\ -x-y+z=2& \end{cases}$
$--------------$
$3z=9\ \parallel:3$
$z=3$
$+\begin{cases} -x-y+3=2&\\ 2x+y+3=6& \end{cases}$
$--------------$

$x=2$

sijoitetaan x ja z johonkin ja ratkaistaan y

$-x-y+z=2$
$-2-y+3=2$
$-y=1$
$y=-1$

$\begin{cases} x=2&\\ y=-1&\\ z=3& \end{cases}$
$tarkistetaan$
$\begin{cases} 2-1+6=7&T\\ -2+1+3=2&T\\ 4-1+3=6&T \end{cases}$
b)
$\begin{cases} 2x+y+z=4&\left(1\right)\\ x+2y+3z=8&\left(2\right)\\ 3x+2y+z=4&\left(3\right) \end{cases}$
$\begin{cases} 2x+y+z=4&\\ x+2y+3z=8&\parallel\cdot\left(-2\right) \end{cases}$
$+\begin{cases} 2x+y+z=4&\\ -2x-4y-6z=-16& \end{cases}$
$-------------$
$-3y-5z=-12$

$\begin{cases} x+2y+3z=8&\parallel\cdot\left(-3\right)\\ 3x+2y+z=4& \end{cases}$
$+\begin{cases} -3x-6y-9z=-24&\\ 3x+2y+z=4& \end{cases}$
$-------------$
$-4y-8z=-20$

$\begin{cases} -3y-5z=-12&\parallel\cdot\left(-4\right)\\ -4y-8z=-20&\parallel\cdot3 \end{cases}$
$\begin{cases} 12y+20z=48&\\ -12y-24z=-60& \end{cases}$
$-4z=-12\ \parallel:\left(-4\right)$
$z=3$

$-3y-5\cdot3=-12$
$-3y=3$
$y=-1$
$2x+y+z=4$
$2x-1+3=4$
$2x=2$
$x=1$

$\begin{cases} 2-1+3=4&T\\ 1-2+9=8&T\\ 3-2+3=4&T \end{cases}$