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

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

Whakaoti mō x, y, z

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

$$y=\frac{2}{3}\approx 0.666666667$$

$$z = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te 3x+2y+z=4 mō z.

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

Whakakapia te -3x-2y+4 mō te z i te whārite tuarua me te tuatoru.

$$x+y+3\left(-3x-2y+4\right)=6 2x-y+6\left(-3x-2y+4\right)=10$$

Me whakaoti ēnei whārite mō y me x takitahi.

$$y=\frac{6}{5}-\frac{8}{5}x x=-\frac{13}{16}y+\frac{7}{8}$$

Whakakapia te \frac{6}{5}-\frac{8}{5}x mō te y i te whārite x=-\frac{13}{16}y+\frac{7}{8}.

$$x=-\frac{13}{16}\left(\frac{6}{5}-\frac{8}{5}x\right)+\frac{7}{8}$$

Me whakaoti te x=-\frac{13}{16}\left(\frac{6}{5}-\frac{8}{5}x\right)+\frac{7}{8} mō x.

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

Whakakapia te \frac{1}{3} mō te x i te whārite y=\frac{6}{5}-\frac{8}{5}x.

$$y=\frac{6}{5}-\frac{8}{5}\times \frac{1}{3}$$

Tātaitia te y i te y=\frac{6}{5}-\frac{8}{5}\times \frac{1}{3}.

$$y=\frac{2}{3}$$

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

$$z=-3\times \frac{1}{3}-2\times \frac{2}{3}+4$$

Tātaitia te z i te z=-3\times \frac{1}{3}-2\times \frac{2}{3}+4.

$$z=\frac{5}{3}$$

Kua oti te pūnaha te whakatau.

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