सोडोवचें {l}{1.6x-0.6y+2.7z=4.27}{3.5x-5.4y+7.3z=11.84}{0.3x+1.6y-3.1z=-4.78}

$$\left. \begin{array} { l } { 1.6 x - 0.6 y + 2.7 z = 4.27 } \\ { 3.5 x - 5.4 y + 7.3 z = 11.84 } \\ { 0.3 x + 1.6 y - 3.1 z = - 4.78 } \end{array} \right.$$

x, y, z खातीर सोडोवचें

$$x=0.1$$

$$y=-0.1$$

$$z=1.5$$

बदली वापरून संक्षिप्त पांवडे

x खातीर 1.6x-0.6y+2.7z=4.27 सोडोवचो.

$$x=0.375y-1.6875z+2.66875$$

दुस-या आनी तिस-या समिकरणांत x खातीर 0.375y-1.6875z+2.66875 बदलपी घेवचो.

$$3.5\left(0.375y-1.6875z+2.66875\right)-5.4y+7.3z=11.84 0.3\left(0.375y-1.6875z+2.66875\right)+1.6y-3.1z=-4.78$$

अनुक्रमान y आनी z खातीर हीं समिकरणां सोडोवचीं.

$$y=\frac{223}{654}z-\frac{1333}{2180} z=\frac{274}{577}y+\frac{8929}{5770}$$

z=\frac{274}{577}y+\frac{8929}{5770} ह्या समिकरणांत y खातीर \frac{223}{654}z-\frac{1333}{2180} बदलपी घेवचो.

$$z=\frac{274}{577}\left(\frac{223}{654}z-\frac{1333}{2180}\right)+\frac{8929}{5770}$$

z खातीर z=\frac{274}{577}\left(\frac{223}{654}z-\frac{1333}{2180}\right)+\frac{8929}{5770} सोडोवचो.

$$z=1.5$$

y=\frac{223}{654}z-\frac{1333}{2180} ह्या समिकरणांत z खातीर 1.5 बदलपी घेवचो.

$$y=\frac{223}{654}\times 1.5-\frac{1333}{2180}$$

y=\frac{223}{654}\times 1.5-\frac{1333}{2180} तल्यान y मेजचो.

$$y=-0.1$$

y आनी 1.5 ह्या समिकरणांत z खातीर -0.1 बदलपी घेवचो x=0.375y-1.6875z+2.66875.

$$x=0.375\left(-0.1\right)-1.6875\times 1.5+2.66875$$

x=0.375\left(-0.1\right)-1.6875\times 1.5+2.66875 तल्यान x मेजचो.

$$x=0.1$$

प्रणाली आतां सुटावी जाली.

$$x=0.1 y=-0.1 z=1.5$$