Réitigh {l}{3x+2y+5z=2}{5x-3y-2z=4}{2x-5y-3z=14}

$$\left. \begin{array} { l } { 3 x + 2 y + 5 z = 2 } \\ { 5 x - 3 y - 2 z = 4 } \\ { 2 x - 5 y - 3 z = 14 } \end{array} \right.$$

Réitigh do x,y,z.

$$x=-1$$

$$y=-5$$

$$z=3$$

Céimeanna gearra ag baint úsáid as ionadú

Réitigh 3x+2y+5z=2 do x.

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

Cuir -\frac{2}{3}y-\frac{5}{3}z+\frac{2}{3} in ionad x sa dara agus sa tríú cothromóid.

$$5\left(-\frac{2}{3}y-\frac{5}{3}z+\frac{2}{3}\right)-3y-2z=4 2\left(-\frac{2}{3}y-\frac{5}{3}z+\frac{2}{3}\right)-5y-3z=14$$

Réitigh na cothromóidí seo do y agus z faoi seach.

$$y=-\frac{2}{19}-\frac{31}{19}z z=-2-y$$

Cuir -\frac{2}{19}-\frac{31}{19}z in ionad y sa chothromóid z=-2-y.

$$z=-2-\left(-\frac{2}{19}-\frac{31}{19}z\right)$$

Réitigh z=-2-\left(-\frac{2}{19}-\frac{31}{19}z\right) do z.

$$z=3$$

Cuir 3 in ionad z sa chothromóid y=-\frac{2}{19}-\frac{31}{19}z.

$$y=-\frac{2}{19}-\frac{31}{19}\times 3$$

Ríomh y ó y=-\frac{2}{19}-\frac{31}{19}\times 3.

$$y=-5$$

Cuir -5 in ionad y agus 3 in ionad z sa chothromóid x=-\frac{2}{3}y-\frac{5}{3}z+\frac{2}{3}.

$$x=-\frac{2}{3}\left(-5\right)-\frac{5}{3}\times 3+\frac{2}{3}$$

Ríomh x ó x=-\frac{2}{3}\left(-5\right)-\frac{5}{3}\times 3+\frac{2}{3}.

$$x=-1$$

Tá an córas réitithe anois.

$$x=-1 y=-5 z=3$$