Whakaoti i te {l}{x+y+z=6}{x+2y+3z=14}{x+3y+9z=34}

$$\left\{ \begin{array} { l } { x + y + z = 6 } \\ { x + 2 y + 3 z = 14 } \\ { x + 3 y + 9 z = 34 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=1$$

$$y=2$$

$$z=3$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te x+y+z=6 mō x.

$$x=-y-z+6$$

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

$$-y-z+6+2y+3z=14 -y-z+6+3y+9z=34$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=8-2z z=\frac{7}{2}-\frac{1}{4}y$$

Whakakapia te 8-2z mō te y i te whārite z=\frac{7}{2}-\frac{1}{4}y.

$$z=\frac{7}{2}-\frac{1}{4}\left(8-2z\right)$$

Me whakaoti te z=\frac{7}{2}-\frac{1}{4}\left(8-2z\right) mō z.

$$z=3$$

Whakakapia te 3 mō te z i te whārite y=8-2z.

$$y=8-2\times 3$$

Tātaitia te y i te y=8-2\times 3.

$$y=2$$

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

$$x=-2-3+6$$

Tātaitia te x i te x=-2-3+6.

$$x=1$$

Kua oti te pūnaha te whakatau.

$$x=1 y=2 z=3$$