सोडोवचें {l}{4x+2y-2z=-8}{-6x+4y+2z=0}{2x+2y+12z=60}

$$\left\{ \begin{array} { l } { 4 x + 2 y - 2 z = - 8 } \\ { - 6 x + 4 y + 2 z = 0 } \\ { 2 x + 2 y + 12 z = 60 } \end{array} \right.$$

x, y, z खातीर सोडोवचें

$$x=1$$

$$y=-1$$

$$z=5$$

बदली वापरून संक्षिप्त पांवडे

x खातीर 4x+2y-2z=-8 सोडोवचो.

$$x=-2-\frac{1}{2}y+\frac{1}{2}z$$

दुस-या आनी तिस-या समिकरणांत x खातीर -2-\frac{1}{2}y+\frac{1}{2}z बदलपी घेवचो.

$$-6\left(-2-\frac{1}{2}y+\frac{1}{2}z\right)+4y+2z=0 2\left(-2-\frac{1}{2}y+\frac{1}{2}z\right)+2y+12z=60$$

अनुक्रमान y आनी z खातीर हीं समिकरणां सोडोवचीं.

$$y=-\frac{12}{7}+\frac{1}{7}z z=\frac{64}{13}-\frac{1}{13}y$$

z=\frac{64}{13}-\frac{1}{13}y ह्या समिकरणांत y खातीर -\frac{12}{7}+\frac{1}{7}z बदलपी घेवचो.

$$z=\frac{64}{13}-\frac{1}{13}\left(-\frac{12}{7}+\frac{1}{7}z\right)$$

z खातीर z=\frac{64}{13}-\frac{1}{13}\left(-\frac{12}{7}+\frac{1}{7}z\right) सोडोवचो.

$$z=5$$

y=-\frac{12}{7}+\frac{1}{7}z ह्या समिकरणांत z खातीर 5 बदलपी घेवचो.

$$y=-\frac{12}{7}+\frac{1}{7}\times 5$$

y=-\frac{12}{7}+\frac{1}{7}\times 5 तल्यान y मेजचो.

$$y=-1$$

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

$$x=-2-\frac{1}{2}\left(-1\right)+\frac{1}{2}\times 5$$

x=-2-\frac{1}{2}\left(-1\right)+\frac{1}{2}\times 5 तल्यान x मेजचो.

$$x=1$$

प्रणाली आतां सुटावी जाली.

$$x=1 y=-1 z=5$$