Whakaoti i te {l}{x-2y+3z=12}{2x-y-2z=5}{2x+2y-z=4}

$$\left. \begin{array} { l } { x - 2 y + 3 z = 12 } \\ { 2 x - y - 2 z = 5 } \\ { 2 x + 2 y - z = 4 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=4$$

$$y=-1$$

$$z=2$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te x-2y+3z=12 mō x.

$$x=2y-3z+12$$

Whakakapia te 2y-3z+12 mō te x i te whārite tuarua me te tuatoru.

$$2\left(2y-3z+12\right)-y-2z=5 2\left(2y-3z+12\right)+2y-z=4$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=\frac{8}{3}z-\frac{19}{3} z=\frac{20}{7}+\frac{6}{7}y$$

Whakakapia te \frac{8}{3}z-\frac{19}{3} mō te y i te whārite z=\frac{20}{7}+\frac{6}{7}y.

$$z=\frac{20}{7}+\frac{6}{7}\left(\frac{8}{3}z-\frac{19}{3}\right)$$

Me whakaoti te z=\frac{20}{7}+\frac{6}{7}\left(\frac{8}{3}z-\frac{19}{3}\right) mō z.

$$z=2$$

Whakakapia te 2 mō te z i te whārite y=\frac{8}{3}z-\frac{19}{3}.

$$y=\frac{8}{3}\times 2-\frac{19}{3}$$

Tātaitia te y i te y=\frac{8}{3}\times 2-\frac{19}{3}.

$$y=-1$$

Whakakapia te -1 mō te y me te 2 mō z i te whārite x=2y-3z+12.

$$x=2\left(-1\right)-3\times 2+12$$

Tātaitia te x i te x=2\left(-1\right)-3\times 2+12.

$$x=4$$

Kua oti te pūnaha te whakatau.

$$x=4 y=-1 z=2$$