Whakaoti i te {l}{x-2y+3z=10}{2x+y-6z=1}{4x-2y-9z=15}

$$\left\{ \begin{array} { l } { x - 2 y + 3 z = 10 } \\ { 2 x + y - 6 z = 1 } \\ { 4 x - 2 y - 9 z = 15 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=3$$

$$y=-3$$

$$z=\frac{1}{3}\approx 0.333333333$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te x-2y+3z=10 mō x.

$$x=2y-3z+10$$

Whakakapia te 2y-3z+10 mō te x i te whārite tuarua me te tuatoru.

$$2\left(2y-3z+10\right)+y-6z=1 4\left(2y-3z+10\right)-2y-9z=15$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=\frac{12}{5}z-\frac{19}{5} z=\frac{2}{7}y+\frac{25}{21}$$

Whakakapia te \frac{12}{5}z-\frac{19}{5} mō te y i te whārite z=\frac{2}{7}y+\frac{25}{21}.

$$z=\frac{2}{7}\left(\frac{12}{5}z-\frac{19}{5}\right)+\frac{25}{21}$$

Me whakaoti te z=\frac{2}{7}\left(\frac{12}{5}z-\frac{19}{5}\right)+\frac{25}{21} mō z.

$$z=\frac{1}{3}$$

Whakakapia te \frac{1}{3} mō te z i te whārite y=\frac{12}{5}z-\frac{19}{5}.

$$y=\frac{12}{5}\times \frac{1}{3}-\frac{19}{5}$$

Tātaitia te y i te y=\frac{12}{5}\times \frac{1}{3}-\frac{19}{5}.

$$y=-3$$

Whakakapia te -3 mō te y me te \frac{1}{3} mō z i te whārite x=2y-3z+10.

$$x=2\left(-3\right)-3\times \frac{1}{3}+10$$

Tātaitia te x i te x=2\left(-3\right)-3\times \frac{1}{3}+10.

$$x=3$$

Kua oti te pūnaha te whakatau.

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