Whakaoti i te {l}{3x-y+z=9}{2x+y-2z=5}{-x+4y-z=0}

$$\left. \begin{array}{l}{ 3 x - y + z = 9 }\\{ 2 x + y - 2 z = 5 }\\{ - x + 4 y - z = 0 }\end{array} \right.$$

Whakaoti mō x, y, z

$$x=3$$

$$y=1$$

$$z=1$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te 3x-y+z=9 mō y.

$$y=3x+z-9$$

Whakakapia te 3x+z-9 mō te y i te whārite tuarua me te tuatoru.

$$2x+3x+z-9-2z=5 -x+4\left(3x+z-9\right)-z=0$$

Me whakaoti ēnei whārite mō x me z takitahi.

$$x=\frac{14}{5}+\frac{1}{5}z z=-\frac{11}{3}x+12$$

Whakakapia te \frac{14}{5}+\frac{1}{5}z mō te x i te whārite z=-\frac{11}{3}x+12.

$$z=-\frac{11}{3}\left(\frac{14}{5}+\frac{1}{5}z\right)+12$$

Me whakaoti te z=-\frac{11}{3}\left(\frac{14}{5}+\frac{1}{5}z\right)+12 mō z.

$$z=1$$

Whakakapia te 1 mō te z i te whārite x=\frac{14}{5}+\frac{1}{5}z.

$$x=\frac{14}{5}+\frac{1}{5}\times 1$$

Tātaitia te x i te x=\frac{14}{5}+\frac{1}{5}\times 1.

$$x=3$$

Whakakapia te 3 mō te x me te 1 mō z i te whārite y=3x+z-9.

$$y=3\times 3+1-9$$

Tātaitia te y i te y=3\times 3+1-9.

$$y=1$$

Kua oti te pūnaha te whakatau.

$$x=3 y=1 z=1$$