सोडोवचें {l}{x+y-3z+t=2c}{3x-y+z-t=2a}{-x+3y-z+t=2b}

$$\left\{ \begin{array} { l } { x + y - 3 z + t = 2 c } \\ { 3 x - y + z - t = 2 a } \\ { - x + 3 y - z + t = 2 b } \end{array} \right.$$

x, y, z खातीर सोडोवचें

$$x=\frac{t+b+c+4a}{6}$$

$$y=\frac{-t+2a+5b-c}{6}$$

$$z=\frac{t+a+b-2c}{3}$$

बदली वापरून संक्षिप्त पांवडे

x खातीर x+y-3z+t=2c सोडोवचो.

$$x=-y+3z-t+2c$$

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

$$3\left(-y+3z-t+2c\right)-y+z-t=2a -\left(-y+3z-t+2c\right)+3y-z+t=2b$$

अनुक्रमान y आनी z खातीर हीं समिकरणां सोडोवचीं.

$$y=-t+\frac{5}{2}z-\frac{1}{2}a+\frac{3}{2}c z=y-\frac{1}{2}b-\frac{1}{2}c+\frac{1}{2}t$$

z=y-\frac{1}{2}b-\frac{1}{2}c+\frac{1}{2}t ह्या समिकरणांत y खातीर -t+\frac{5}{2}z-\frac{1}{2}a+\frac{3}{2}c बदलपी घेवचो.

$$z=-t+\frac{5}{2}z-\frac{1}{2}a+\frac{3}{2}c-\frac{1}{2}b-\frac{1}{2}c+\frac{1}{2}t$$

z खातीर z=-t+\frac{5}{2}z-\frac{1}{2}a+\frac{3}{2}c-\frac{1}{2}b-\frac{1}{2}c+\frac{1}{2}t सोडोवचो.

$$z=\frac{1}{3}t-\frac{2}{3}c+\frac{1}{3}a+\frac{1}{3}b$$

y=-t+\frac{5}{2}z-\frac{1}{2}a+\frac{3}{2}c ह्या समिकरणांत z खातीर \frac{1}{3}t-\frac{2}{3}c+\frac{1}{3}a+\frac{1}{3}b बदलपी घेवचो.

$$y=-t+\frac{5}{2}\left(\frac{1}{3}t-\frac{2}{3}c+\frac{1}{3}a+\frac{1}{3}b\right)-\frac{1}{2}a+\frac{3}{2}c$$

y=-t+\frac{5}{2}\left(\frac{1}{3}t-\frac{2}{3}c+\frac{1}{3}a+\frac{1}{3}b\right)-\frac{1}{2}a+\frac{3}{2}c तल्यान y मेजचो.

$$y=-\frac{1}{6}t-\frac{1}{6}c+\frac{1}{3}a+\frac{5}{6}b$$

y आनी \frac{1}{3}t-\frac{2}{3}c+\frac{1}{3}a+\frac{1}{3}b ह्या समिकरणांत z खातीर -\frac{1}{6}t-\frac{1}{6}c+\frac{1}{3}a+\frac{5}{6}b बदलपी घेवचो x=-y+3z-t+2c.

$$x=-\left(-\frac{1}{6}t-\frac{1}{6}c+\frac{1}{3}a+\frac{5}{6}b\right)+3\left(\frac{1}{3}t-\frac{2}{3}c+\frac{1}{3}a+\frac{1}{3}b\right)-t+2c$$

x=-\left(-\frac{1}{6}t-\frac{1}{6}c+\frac{1}{3}a+\frac{5}{6}b\right)+3\left(\frac{1}{3}t-\frac{2}{3}c+\frac{1}{3}a+\frac{1}{3}b\right)-t+2c तल्यान x मेजचो.

$$x=\frac{1}{6}t+\frac{1}{6}c+\frac{2}{3}a+\frac{1}{6}b$$

प्रणाली आतां सुटावी जाली.

$$x=\frac{1}{6}t+\frac{1}{6}c+\frac{2}{3}a+\frac{1}{6}b y=-\frac{1}{6}t-\frac{1}{6}c+\frac{1}{3}a+\frac{5}{6}b z=\frac{1}{3}t-\frac{2}{3}c+\frac{1}{3}a+\frac{1}{3}b$$