सोडोवचें {l}{10x+10y-20z=60}{15x+20y+20z=-25}{-5x+30y-10z=45}

$$\left\{ \begin{array} { l } { 10 x + 10 y - 20 z = 60 } \\ { 15 x + 20 y + 20 z = - 25 } \\ { - 5 x + 30 y - 10 z = 45 } \end{array} \right.$$

x, y, z खातीर सोडोवचें

$$x=\frac{17}{37}\approx 0.459459459$$

$$y=\frac{29}{37}\approx 0.783783784$$

$$z = -\frac{88}{37} = -2\frac{14}{37} \approx -2.378378378$$

बदली वापरून संक्षिप्त पांवडे

x खातीर 10x+10y-20z=60 सोडोवचो.

$$x=6-y+2z$$

दुस-या आनी तिस-या समिकरणांत x खातीर 6-y+2z बदलपी घेवचो.

$$15\left(6-y+2z\right)+20y+20z=-25 -5\left(6-y+2z\right)+30y-10z=45$$

अनुक्रमान y आनी z खातीर हीं समिकरणां सोडोवचीं.

$$y=-23-10z z=-\frac{15}{4}+\frac{7}{4}y$$

z=-\frac{15}{4}+\frac{7}{4}y ह्या समिकरणांत y खातीर -23-10z बदलपी घेवचो.

$$z=-\frac{15}{4}+\frac{7}{4}\left(-23-10z\right)$$

z खातीर z=-\frac{15}{4}+\frac{7}{4}\left(-23-10z\right) सोडोवचो.

$$z=-\frac{88}{37}$$

y=-23-10z ह्या समिकरणांत z खातीर -\frac{88}{37} बदलपी घेवचो.

$$y=-23-10\left(-\frac{88}{37}\right)$$

y=-23-10\left(-\frac{88}{37}\right) तल्यान y मेजचो.

$$y=\frac{29}{37}$$

y आनी -\frac{88}{37} ह्या समिकरणांत z खातीर \frac{29}{37} बदलपी घेवचो x=6-y+2z.

$$x=6-\frac{29}{37}+2\left(-\frac{88}{37}\right)$$

x=6-\frac{29}{37}+2\left(-\frac{88}{37}\right) तल्यान x मेजचो.

$$x=\frac{17}{37}$$

प्रणाली आतां सुटावी जाली.

$$x=\frac{17}{37} y=\frac{29}{37} z=-\frac{88}{37}$$