सोडोवचें {l}{x+y+z=7}{-14y-7/1z=0}{3x+6y-2z=0}

$$\left\{ \begin{array} { l } { x + y + z = 7 } \\ { - 14 y - \frac { 7 } { 1 } z = 0 } \\ { 3 x + 6 y - 2 z = 0 } \end{array} \right.$$

x, y, z खातीर सोडोवचें

$$x = \frac{70}{13} = 5\frac{5}{13} \approx 5.384615385$$

$$y = -\frac{21}{13} = -1\frac{8}{13} \approx -1.615384615$$

$$z = \frac{42}{13} = 3\frac{3}{13} \approx 3.230769231$$

बदली वापरून संक्षिप्त पांवडे

x खातीर x+y+z=7 सोडोवचो.

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

3x+6y-2z=0 ह्या समिकरणांत x खातीर -y-z+7 बदलपी घेवचो.

$$3\left(-y-z+7\right)+6y-2z=0$$

y खातीर दुसरें समिकरण आनी z खातीर तिसरें समिकरण सोडोवचें.

$$y=-\frac{1}{2}z z=\frac{21}{5}+\frac{3}{5}y$$

z=\frac{21}{5}+\frac{3}{5}y ह्या समिकरणांत y खातीर -\frac{1}{2}z बदलपी घेवचो.

$$z=\frac{21}{5}+\frac{3}{5}\left(-\frac{1}{2}\right)z$$

z खातीर z=\frac{21}{5}+\frac{3}{5}\left(-\frac{1}{2}\right)z सोडोवचो.

$$z=\frac{42}{13}$$

y=-\frac{1}{2}z ह्या समिकरणांत z खातीर \frac{42}{13} बदलपी घेवचो.

$$y=-\frac{1}{2}\times \frac{42}{13}$$

y=-\frac{1}{2}\times \frac{42}{13} तल्यान y मेजचो.

$$y=-\frac{21}{13}$$

y आनी \frac{42}{13} ह्या समिकरणांत z खातीर -\frac{21}{13} बदलपी घेवचो x=-y-z+7.

$$x=-\left(-\frac{21}{13}\right)-\frac{42}{13}+7$$

x=-\left(-\frac{21}{13}\right)-\frac{42}{13}+7 तल्यान x मेजचो.

$$x=\frac{70}{13}$$

प्रणाली आतां सुटावी जाली.

$$x=\frac{70}{13} y=-\frac{21}{13} z=\frac{42}{13}$$