सोडोवचें {l}{x+y-2y=-3}{5x-2y+7z=22}{2x-5y+4z=4}

$$\left. \begin{array} { l } { x + y - 2 y = - 3 } \\ { 5 x - 2 y + 7 z = 22 } \\ { 2 x - 5 y + 4 z = 4 } \end{array} \right.$$

x, y, z खातीर सोडोवचें

$$x=-\frac{7}{11}\approx -0.636363636$$

$$y = \frac{26}{11} = 2\frac{4}{11} \approx 2.363636364$$

$$z = \frac{47}{11} = 4\frac{3}{11} \approx 4.272727273$$

बदली वापरून संक्षिप्त पांवडे

x खातीर x+y-2y=-3 सोडोवचो.

$$x=y-3$$

दुस-या आनी तिस-या समिकरणांत x खातीर y-3 बदलपी घेवचो.

$$5\left(y-3\right)-2y+7z=22 2\left(y-3\right)-5y+4z=4$$

अनुक्रमान y आनी z खातीर हीं समिकरणां सोडोवचीं.

$$y=\frac{37}{3}-\frac{7}{3}z z=\frac{3}{4}y+\frac{5}{2}$$

z=\frac{3}{4}y+\frac{5}{2} ह्या समिकरणांत y खातीर \frac{37}{3}-\frac{7}{3}z बदलपी घेवचो.

$$z=\frac{3}{4}\left(\frac{37}{3}-\frac{7}{3}z\right)+\frac{5}{2}$$

z खातीर z=\frac{3}{4}\left(\frac{37}{3}-\frac{7}{3}z\right)+\frac{5}{2} सोडोवचो.

$$z=\frac{47}{11}$$

y=\frac{37}{3}-\frac{7}{3}z ह्या समिकरणांत z खातीर \frac{47}{11} बदलपी घेवचो.

$$y=\frac{37}{3}-\frac{7}{3}\times \frac{47}{11}$$

y=\frac{37}{3}-\frac{7}{3}\times \frac{47}{11} तल्यान y मेजचो.

$$y=\frac{26}{11}$$

x=y-3 ह्या समिकरणांत y खातीर \frac{26}{11} बदलपी घेवचो.

$$x=\frac{26}{11}-3$$

x=\frac{26}{11}-3 तल्यान x मेजचो.

$$x=-\frac{7}{11}$$

प्रणाली आतां सुटावी जाली.

$$x=-\frac{7}{11} y=\frac{26}{11} z=\frac{47}{11}$$