Whakaoti i te {l}{2x+4y+6z=-12}{2x-3y-4z=15}{3x+4y+5z=-8}

$$\left\{ \begin{array} { l } { 2 x + 4 y + 6 z = - 12 } \\ { 2 x - 3 y - 4 z = 15 } \\ { 3 x + 4 y + 5 z = - 8 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=2$$

$$y=-1$$

$$z=-2$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te 2x+4y+6z=-12 mō x.

$$x=-6-2y-3z$$

Whakakapia te -6-2y-3z mō te x i te whārite tuarua me te tuatoru.

$$2\left(-6-2y-3z\right)-3y-4z=15 3\left(-6-2y-3z\right)+4y+5z=-8$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=-\frac{27}{7}-\frac{10}{7}z z=-\frac{5}{2}-\frac{1}{2}y$$

Whakakapia te -\frac{27}{7}-\frac{10}{7}z mō te y i te whārite z=-\frac{5}{2}-\frac{1}{2}y.

$$z=-\frac{5}{2}-\frac{1}{2}\left(-\frac{27}{7}-\frac{10}{7}z\right)$$

Me whakaoti te z=-\frac{5}{2}-\frac{1}{2}\left(-\frac{27}{7}-\frac{10}{7}z\right) mō z.

$$z=-2$$

Whakakapia te -2 mō te z i te whārite y=-\frac{27}{7}-\frac{10}{7}z.

$$y=-\frac{27}{7}-\frac{10}{7}\left(-2\right)$$

Tātaitia te y i te y=-\frac{27}{7}-\frac{10}{7}\left(-2\right).

$$y=-1$$

Whakakapia te -1 mō te y me te -2 mō z i te whārite x=-6-2y-3z.

$$x=-6-2\left(-1\right)-3\left(-2\right)$$

Tātaitia te x i te x=-6-2\left(-1\right)-3\left(-2\right).

$$x=2$$

Kua oti te pūnaha te whakatau.

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