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

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

x, y, z खातीर सोडोवचें

$$x=-\frac{8}{9}\approx -0.888888889$$

$$y = \frac{23}{18} = 1\frac{5}{18} \approx 1.277777778$$

$$z=-\frac{7}{18}\approx -0.388888889$$

बदली वापरून संक्षिप्त पांवडे

z खातीर -4x+3y+z=7 सोडोवचो.

$$z=4x-3y+7$$

दुस-या आनी तिस-या समिकरणांत z खातीर 4x-3y+7 बदलपी घेवचो.

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

अनुक्रमान y आनी x खातीर हीं समिकरणां सोडोवचीं.

$$y=\frac{19}{10}+\frac{7}{10}x x=y-\frac{13}{6}$$

x=y-\frac{13}{6} ह्या समिकरणांत y खातीर \frac{19}{10}+\frac{7}{10}x बदलपी घेवचो.

$$x=\frac{19}{10}+\frac{7}{10}x-\frac{13}{6}$$

x खातीर x=\frac{19}{10}+\frac{7}{10}x-\frac{13}{6} सोडोवचो.

$$x=-\frac{8}{9}$$

y=\frac{19}{10}+\frac{7}{10}x ह्या समिकरणांत x खातीर -\frac{8}{9} बदलपी घेवचो.

$$y=\frac{19}{10}+\frac{7}{10}\left(-\frac{8}{9}\right)$$

y=\frac{19}{10}+\frac{7}{10}\left(-\frac{8}{9}\right) तल्यान y मेजचो.

$$y=\frac{23}{18}$$

y आनी -\frac{8}{9} ह्या समिकरणांत x खातीर \frac{23}{18} बदलपी घेवचो z=4x-3y+7.

$$z=4\left(-\frac{8}{9}\right)-3\times \frac{23}{18}+7$$

z=4\left(-\frac{8}{9}\right)-3\times \frac{23}{18}+7 तल्यान z मेजचो.

$$z=-\frac{7}{18}$$

प्रणाली आतां सुटावी जाली.

$$x=-\frac{8}{9} y=\frac{23}{18} z=-\frac{7}{18}$$