Sistema a più incognite 8

$\Bigg \{ \begin{array}{ll} \frac{2y+x-z}3 + \frac 15x=\frac 45 \\ 2y-\frac{x+z}2=3 \\ 2(x-y)-\frac 13z=-2 \end{array}$

$\Bigg \{ \begin{array}{ll} \frac{10y+5x-5z+3x}{15}=\frac {12}{15} \\ \frac{4y-x-z} 2=\frac 62 \\ \frac {6x-6y-z}{3}=-\frac 6 2 \end{array}$

$\Bigg \{ \begin{array}{ll} 8x +10y-5z=12 \\ -x+4y-z= 6 \\ 6x-6y-z=- 6 \end{array}$

$\Delta=\mathrm {det} \begin{vmatrix} 8 & 10 & -5 \\ -1 & 4 & -1 \\ 6 & -6 & -1 \end{vmatrix}=$

$=(-32-60-30)-(48+10-120)=-122+62=-60$

$\Delta_x=\mathrm {det} \begin{vmatrix} 12 & 10 & -5 \\ 6 & 4 & -1 \\ -6 & -6 & -1 \end{vmatrix}=$

$=(-48+60+180)-(72-60+120)=192-132=60$

$\Delta_y=\mathrm {det} \begin{vmatrix} 8 & 12 & -5 \\ -1 & 6 & -1 \\ 6 & -6 & -1 \end{vmatrix}=$

$=(-48-72-30)-(48+12-180)=-150+120=-30$

$\Delta_z=\mathrm {det} \begin{vmatrix} 8 & 10 & 12 \\ -1 & 4 & 6 \\ 6 & -6 & -6 \end{vmatrix}=$

$=(-192+360+72)-(-288+60+288)=240-60=180$

$x=\frac {\Delta_x}{\Delta}=\frac {60}{-60}=-1$

$y=\frac {\Delta_y}{\Delta}=\frac {-30}{-60}=\frac 1 2$

$z=\frac {\Delta_z}{\Delta}=\frac {180}{-60}=-3$

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