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

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

x, y, z खातीर सोडोवचें

$$x=-\frac{5}{11}\approx -0.454545455$$

$$y = -\frac{13}{11} = -1\frac{2}{11} \approx -1.181818182$$

$$z=\frac{3}{11}\approx 0.272727273$$

बदली वापरून संक्षिप्त पांवडे

समिकरणांचो क्रम परत लावचो.

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

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.

$$y=-\frac{1}{3}x-\frac{4}{3} x=\frac{2}{3}y+\frac{1}{3}$$

x=\frac{2}{3}y+\frac{1}{3} ह्या समिकरणांत y खातीर -\frac{1}{3}x-\frac{4}{3} बदलपी घेवचो.

$$x=\frac{2}{3}\left(-\frac{1}{3}x-\frac{4}{3}\right)+\frac{1}{3}$$

x खातीर x=\frac{2}{3}\left(-\frac{1}{3}x-\frac{4}{3}\right)+\frac{1}{3} सोडोवचो.

$$x=-\frac{5}{11}$$

y=-\frac{1}{3}x-\frac{4}{3} ह्या समिकरणांत x खातीर -\frac{5}{11} बदलपी घेवचो.

$$y=-\frac{1}{3}\left(-\frac{5}{11}\right)-\frac{4}{3}$$

y=-\frac{1}{3}\left(-\frac{5}{11}\right)-\frac{4}{3} तल्यान y मेजचो.

$$y=-\frac{13}{11}$$

y आनी -\frac{5}{11} ह्या समिकरणांत x खातीर -\frac{13}{11} बदलपी घेवचो z=-4x+3y+2.

$$z=-4\left(-\frac{5}{11}\right)+3\left(-\frac{13}{11}\right)+2$$

z=-4\left(-\frac{5}{11}\right)+3\left(-\frac{13}{11}\right)+2 तल्यान z मेजचो.

$$z=\frac{3}{11}$$

प्रणाली आतां सुटावी जाली.

$$x=-\frac{5}{11} y=-\frac{13}{11} z=\frac{3}{11}$$