Whakaoti i te {l}{3x-y-2z=-15}{x+3y-z=2}{2x+y-5z=-3}

$$\left\{ \begin{array} { l } { 3 x - y - 2 z = - 15 } \\ { x + 3 y - z = 2 } \\ { 2 x + y - 5 z = - 3 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=-5$$

$$y=2$$

$$z=-1$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te 3x-y-2z=-15 mō y.

$$y=3x-2z+15$$

Whakakapia te 3x-2z+15 mō te y i te whārite tuarua me te tuatoru.

$$x+3\left(3x-2z+15\right)-z=2 2x+3x-2z+15-5z=-3$$

Me whakaoti ēnei whārite mō x me z takitahi.

$$x=\frac{7}{10}z-\frac{43}{10} z=\frac{5}{7}x+\frac{18}{7}$$

Whakakapia te \frac{7}{10}z-\frac{43}{10} mō te x i te whārite z=\frac{5}{7}x+\frac{18}{7}.

$$z=\frac{5}{7}\left(\frac{7}{10}z-\frac{43}{10}\right)+\frac{18}{7}$$

Me whakaoti te z=\frac{5}{7}\left(\frac{7}{10}z-\frac{43}{10}\right)+\frac{18}{7} mō z.

$$z=-1$$

Whakakapia te -1 mō te z i te whārite x=\frac{7}{10}z-\frac{43}{10}.

$$x=\frac{7}{10}\left(-1\right)-\frac{43}{10}$$

Tātaitia te x i te x=\frac{7}{10}\left(-1\right)-\frac{43}{10}.

$$x=-5$$

Whakakapia te -5 mō te x me te -1 mō z i te whārite y=3x-2z+15.

$$y=3\left(-5\right)-2\left(-1\right)+15$$

Tātaitia te y i te y=3\left(-5\right)-2\left(-1\right)+15.

$$y=2$$

Kua oti te pūnaha te whakatau.

$$x=-5 y=2 z=-1$$