सोडोवचें {c}{2x+3y=1}{4x-3y+z=-2}{x-y+z=1}

$$\left\{ \begin{array} { c } { 2 x + 3 y = 1 } \\ { 4 x - 3 y + z = - 2 } \\ { x - y + z = 1 } \end{array} \right.$$

x, y, z खातीर सोडोवचें

$$x=-\frac{7}{13}\approx -0.538461538$$

$$y=\frac{9}{13}\approx 0.692307692$$

$$z = \frac{29}{13} = 2\frac{3}{13} \approx 2.230769231$$

बदली वापरून संक्षिप्त पांवडे

समिकरणांचो क्रम परत लावचो.

$$4x-3y+z=-2 2x+3y=1 x-y+z=1$$

z खातीर 4x-3y+z=-2 सोडोवचो.

$$z=-4x+3y-2$$

x-y+z=1 ह्या समिकरणांत z खातीर -4x+3y-2 बदलपी घेवचो.

$$x-y-4x+3y-2=1$$

y खातीर दुसरें समिकरण आनी x खातीर तिसरें समिकरण सोडोवचें.

$$y=-\frac{2}{3}x+\frac{1}{3} x=\frac{2}{3}y-1$$

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

$$x=\frac{2}{3}\left(-\frac{2}{3}x+\frac{1}{3}\right)-1$$

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

$$x=-\frac{7}{13}$$

y=-\frac{2}{3}x+\frac{1}{3} ह्या समिकरणांत x खातीर -\frac{7}{13} बदलपी घेवचो.

$$y=-\frac{2}{3}\left(-\frac{7}{13}\right)+\frac{1}{3}$$

y=-\frac{2}{3}\left(-\frac{7}{13}\right)+\frac{1}{3} तल्यान y मेजचो.

$$y=\frac{9}{13}$$

y आनी -\frac{7}{13} ह्या समिकरणांत x खातीर \frac{9}{13} बदलपी घेवचो z=-4x+3y-2.

$$z=-4\left(-\frac{7}{13}\right)+3\times \frac{9}{13}-2$$

z=-4\left(-\frac{7}{13}\right)+3\times \frac{9}{13}-2 तल्यान z मेजचो.

$$z=\frac{29}{13}$$

प्रणाली आतां सुटावी जाली.

$$x=-\frac{7}{13} y=\frac{9}{13} z=\frac{29}{13}$$