Question

Rezolvați sistemul x+y+z=6
2x-y+z=3
X+y-2z=-3

Answer 1

$\begin{bmatrix}x+y+z=6\\ 2x-y+z=3\\ x+y-2z=-3\end{bmatrix} = \begin{bmatrix}2\left(6-y-z\right)-y+z=3\\ 6-y-z+y-2z=-3\end{bmatrix} = \begin{bmatrix}-3y-z+12=3\\ -3z+6=-3\end{bmatrix} = \begin{bmatrix}-3y-3+12=3\end{bmatrix} =\\ \\\begin{bmatrix}-3y+9=3\end{bmatrix}$

$-3z+6=-3 \Rightarrow -3z = -3 -6 = -9 \RIghtarrow z= -9 : (-3) =3$

$-3y+9=3 \Rightarrow -3y = 3- 9 \Rightarrow -3y = -6 \Rightarrow y =2$

$x=6-y-z \Rightarrow x=6-2-3 \Rightarrow x = 1$

$x=1,\:z=3,\:y=2$