सोडोवचें {l}{2x+y+z=12}{2x-y+z=7}{x+2y-z=6}

$$\left. \begin{array} { l } { 2 x + y + z = 12 } \\ { 2 x - y + z = 7 } \\ { x + 2 y - z = 6 } \end{array} \right.$$

x, y, z खातीर सोडोवचें

$$x = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

$$y = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

$$z = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

बदली वापरून संक्षिप्त पांवडे

y खातीर 2x+y+z=12 सोडोवचो.

$$y=-2x-z+12$$

दुस-या आनी तिस-या समिकरणांत y खातीर -2x-z+12 बदलपी घेवचो.

$$2x-\left(-2x-z+12\right)+z=7 x+2\left(-2x-z+12\right)-z=6$$

अनुक्रमान x आनी z खातीर हीं समिकरणां सोडोवचीं.

$$x=-\frac{1}{2}z+\frac{19}{4} z=6-x$$

z=6-x ह्या समिकरणांत x खातीर -\frac{1}{2}z+\frac{19}{4} बदलपी घेवचो.

$$z=6-\left(-\frac{1}{2}z+\frac{19}{4}\right)$$

z खातीर z=6-\left(-\frac{1}{2}z+\frac{19}{4}\right) सोडोवचो.

$$z=\frac{5}{2}$$

x=-\frac{1}{2}z+\frac{19}{4} ह्या समिकरणांत z खातीर \frac{5}{2} बदलपी घेवचो.

$$x=-\frac{1}{2}\times \frac{5}{2}+\frac{19}{4}$$

x=-\frac{1}{2}\times \frac{5}{2}+\frac{19}{4} तल्यान x मेजचो.

$$x=\frac{7}{2}$$

x आनी \frac{5}{2} ह्या समिकरणांत z खातीर \frac{7}{2} बदलपी घेवचो y=-2x-z+12.

$$y=-2\times \frac{7}{2}-\frac{5}{2}+12$$

y=-2\times \frac{7}{2}-\frac{5}{2}+12 तल्यान y मेजचो.

$$y=\frac{5}{2}$$

प्रणाली आतां सुटावी जाली.

$$x=\frac{7}{2} y=\frac{5}{2} z=\frac{5}{2}$$