Whakaoti i te {l}{-2x+y-2z=4}{2x+y=1}{-x+3y-2z=6}

$$\left. \begin{array} { l } { - 2 x + y - 2 z = 4 } \\ { 2 x + y = 1 } \\ { - x + 3 y - 2 z = 6 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=0$$

$$y=1$$

$$z = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te -2x+y-2z=4 mō y.

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

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

$$2x+4+2x+2z=1 -x+3\left(4+2x+2z\right)-2z=6$$

Me whakaoti ēnei whārite mō x me z takitahi.

$$x=-\frac{3}{4}-\frac{1}{2}z z=-\frac{5}{4}x-\frac{3}{2}$$

Whakakapia te -\frac{3}{4}-\frac{1}{2}z mō te x i te whārite z=-\frac{5}{4}x-\frac{3}{2}.

$$z=-\frac{5}{4}\left(-\frac{3}{4}-\frac{1}{2}z\right)-\frac{3}{2}$$

Me whakaoti te z=-\frac{5}{4}\left(-\frac{3}{4}-\frac{1}{2}z\right)-\frac{3}{2} mō z.

$$z=-\frac{3}{2}$$

Whakakapia te -\frac{3}{2} mō te z i te whārite x=-\frac{3}{4}-\frac{1}{2}z.

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

Tātaitia te x i te x=-\frac{3}{4}-\frac{1}{2}\left(-\frac{3}{2}\right).

$$x=0$$

Whakakapia te 0 mō te x me te -\frac{3}{2} mō z i te whārite y=4+2x+2z.

$$y=4+2\times 0+2\left(-\frac{3}{2}\right)$$

Tātaitia te y i te y=4+2\times 0+2\left(-\frac{3}{2}\right).

$$y=1$$

Kua oti te pūnaha te whakatau.

$$x=0 y=1 z=-\frac{3}{2}$$