Whakaoti i te {c}{3x+2y+2z=-2}{2x+y-z=-2}{x-3y+z=0}

$$\left\{ \begin{array} { c } { 3 x + 2 y + 2 z = - 2 } \\ { 2 x + y - z = - 2 } \\ { x - 3 y + z = 0 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=-\frac{10}{13}\approx -0.769230769$$

$$y=-\frac{2}{13}\approx -0.153846154$$

$$z=\frac{4}{13}\approx 0.307692308$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me raupapa anō ngā whārite.

$$2x+y-z=-2 3x+2y+2z=-2 x-3y+z=0$$

Me whakaoti te 2x+y-z=-2 mō y.

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

Whakakapia te -2x+z-2 mō te y i te whārite tuarua me te tuatoru.

$$3x+2\left(-2x+z-2\right)+2z=-2 x-3\left(-2x+z-2\right)+z=0$$

Me whakaoti ēnei whārite mō x me z takitahi.

$$x=4z-2 z=\frac{7}{2}x+3$$

Whakakapia te 4z-2 mō te x i te whārite z=\frac{7}{2}x+3.

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

Me whakaoti te z=\frac{7}{2}\left(4z-2\right)+3 mō z.

$$z=\frac{4}{13}$$

Whakakapia te \frac{4}{13} mō te z i te whārite x=4z-2.

$$x=4\times \frac{4}{13}-2$$

Tātaitia te x i te x=4\times \frac{4}{13}-2.

$$x=-\frac{10}{13}$$

Whakakapia te -\frac{10}{13} mō te x me te \frac{4}{13} mō z i te whārite y=-2x+z-2.

$$y=-2\left(-\frac{10}{13}\right)+\frac{4}{13}-2$$

Tātaitia te y i te y=-2\left(-\frac{10}{13}\right)+\frac{4}{13}-2.

$$y=-\frac{2}{13}$$

Kua oti te pūnaha te whakatau.

$$x=-\frac{10}{13} y=-\frac{2}{13} z=\frac{4}{13}$$