Réitigh {l}{3x+5y+6z=24}{5x+7y+3z=150}{x+y+z=-8}

$$\left. \begin{array} { l } { 3 x + 5 y + 6 z = 24 } \\ { 5 x + 7 y + 3 z = 150 } \\ { x + y + z = - 8 } \end{array} \right.$$

Réitigh do x,y,z.

$$x = -\frac{231}{5} = -46\frac{1}{5} = -46.2$$

$$y = \frac{333}{5} = 66\frac{3}{5} = 66.6$$

$$z = -\frac{142}{5} = -28\frac{2}{5} = -28.4$$

Céimeanna gearra ag baint úsáid as ionadú

Athraigh ord na gcothromóidí.

$$x+y+z=-8 5x+7y+3z=150 3x+5y+6z=24$$

Réitigh x+y+z=-8 do x.

$$x=-y-z-8$$

Cuir -y-z-8 in ionad x sa dara agus sa tríú cothromóid.

$$5\left(-y-z-8\right)+7y+3z=150 3\left(-y-z-8\right)+5y+6z=24$$

Réitigh na cothromóidí seo do y agus z faoi seach.

$$y=95+z z=16-\frac{2}{3}y$$

Cuir 95+z in ionad y sa chothromóid z=16-\frac{2}{3}y.

$$z=16-\frac{2}{3}\left(95+z\right)$$

Réitigh z=16-\frac{2}{3}\left(95+z\right) do z.

$$z=-\frac{142}{5}$$

Cuir -\frac{142}{5} in ionad z sa chothromóid y=95+z.

$$y=95-\frac{142}{5}$$

Ríomh y ó y=95-\frac{142}{5}.

$$y=\frac{333}{5}$$

Cuir \frac{333}{5} in ionad y agus -\frac{142}{5} in ionad z sa chothromóid x=-y-z-8.

$$x=-\frac{333}{5}-\left(-\frac{142}{5}\right)-8$$

Ríomh x ó x=-\frac{333}{5}-\left(-\frac{142}{5}\right)-8.

$$x=-\frac{231}{5}$$

Tá an córas réitithe anois.

$$x=-\frac{231}{5} y=\frac{333}{5} z=-\frac{142}{5}$$