सोडोवचें {l}{3x+2y+z=5}{x+y+5z=3}{x-y+2z=-8}

$$\left. \begin{array} { l } { 3 x + 2 y + z = 5 } \\ { x + y + 5 z = 3 } \\ { x - y + 2 z = - 8 } \end{array} \right.$$

x, y, z खातीर सोडोवचें

$$x = -\frac{52}{25} = -2\frac{2}{25} = -2.08$$

$$y = \frac{142}{25} = 5\frac{17}{25} = 5.68$$

$$z=-\frac{3}{25}=-0.12$$

बदली वापरून संक्षिप्त पांवडे

z खातीर 3x+2y+z=5 सोडोवचो.

$$z=-3x-2y+5$$

दुस-या आनी तिस-या समिकरणांत z खातीर -3x-2y+5 बदलपी घेवचो.

$$x+y+5\left(-3x-2y+5\right)=3 x-y+2\left(-3x-2y+5\right)=-8$$

अनुक्रमान y आनी x खातीर हीं समिकरणां सोडोवचीं.

$$y=\frac{22}{9}-\frac{14}{9}x x=-y+\frac{18}{5}$$

x=-y+\frac{18}{5} ह्या समिकरणांत y खातीर \frac{22}{9}-\frac{14}{9}x बदलपी घेवचो.

$$x=-\left(\frac{22}{9}-\frac{14}{9}x\right)+\frac{18}{5}$$

x खातीर x=-\left(\frac{22}{9}-\frac{14}{9}x\right)+\frac{18}{5} सोडोवचो.

$$x=-\frac{52}{25}$$

y=\frac{22}{9}-\frac{14}{9}x ह्या समिकरणांत x खातीर -\frac{52}{25} बदलपी घेवचो.

$$y=\frac{22}{9}-\frac{14}{9}\left(-\frac{52}{25}\right)$$

y=\frac{22}{9}-\frac{14}{9}\left(-\frac{52}{25}\right) तल्यान y मेजचो.

$$y=\frac{142}{25}$$

y आनी -\frac{52}{25} ह्या समिकरणांत x खातीर \frac{142}{25} बदलपी घेवचो z=-3x-2y+5.

$$z=-3\left(-\frac{52}{25}\right)-2\times \frac{142}{25}+5$$

z=-3\left(-\frac{52}{25}\right)-2\times \frac{142}{25}+5 तल्यान z मेजचो.

$$z=-\frac{3}{25}$$

प्रणाली आतां सुटावी जाली.

$$x=-\frac{52}{25} y=\frac{142}{25} z=-\frac{3}{25}$$