Whakaoti i te {l}{x-2y+z=4}{x-y-4z=1}{x-4y+2z=8}

$$\left. \begin{array} { l } { x - 2 y + z = 4 } \\ { x - y - 4 z = 1 } \\ { x - 4 y + 2 z = 8 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=0$$

$$y = -\frac{17}{9} = -1\frac{8}{9} \approx -1.888888889$$

$$z=\frac{2}{9}\approx 0.222222222$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te x-2y+z=4 mō x.

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

Whakakapia te 2y-z+4 mō te x i te whārite tuarua me te tuatoru.

$$2y-z+4-y-4z=1 2y-z+4-4y+2z=8$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=5z-3 z=4+2y$$

Whakakapia te 5z-3 mō te y i te whārite z=4+2y.

$$z=4+2\left(5z-3\right)$$

Me whakaoti te z=4+2\left(5z-3\right) mō z.

$$z=\frac{2}{9}$$

Whakakapia te \frac{2}{9} mō te z i te whārite y=5z-3.

$$y=5\times \frac{2}{9}-3$$

Tātaitia te y i te y=5\times \frac{2}{9}-3.

$$y=-\frac{17}{9}$$

Whakakapia te -\frac{17}{9} mō te y me te \frac{2}{9} mō z i te whārite x=2y-z+4.

$$x=2\left(-\frac{17}{9}\right)-\frac{2}{9}+4$$

Tātaitia te x i te x=2\left(-\frac{17}{9}\right)-\frac{2}{9}+4.

$$x=0$$

Kua oti te pūnaha te whakatau.

$$x=0 y=-\frac{17}{9} z=\frac{2}{9}$$