Whakaoti i te {l}{2x-y+5z=16}{x-6y+2z=-9}{3x+4y-z=32}

$$\left\{ \begin{array} { l } { 2 x - y + 5 z = 16 } \\ { x - 6 y + 2 z = - 9 } \\ { 3 x + 4 y - z = 32 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=7$$

$$y=3$$

$$z=1$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te 2x-y+5z=16 mō y.

$$y=2x+5z-16$$

Whakakapia te 2x+5z-16 mō te y i te whārite tuarua me te tuatoru.

$$x-6\left(2x+5z-16\right)+2z=-9 3x+4\left(2x+5z-16\right)-z=32$$

Me whakaoti ēnei whārite mō x me z takitahi.

$$x=\frac{105}{11}-\frac{28}{11}z z=-\frac{11}{19}x+\frac{96}{19}$$

Whakakapia te \frac{105}{11}-\frac{28}{11}z mō te x i te whārite z=-\frac{11}{19}x+\frac{96}{19}.

$$z=-\frac{11}{19}\left(\frac{105}{11}-\frac{28}{11}z\right)+\frac{96}{19}$$

Me whakaoti te z=-\frac{11}{19}\left(\frac{105}{11}-\frac{28}{11}z\right)+\frac{96}{19} mō z.

$$z=1$$

Whakakapia te 1 mō te z i te whārite x=\frac{105}{11}-\frac{28}{11}z.

$$x=\frac{105}{11}-\frac{28}{11}$$

Tātaitia te x i te x=\frac{105}{11}-\frac{28}{11}.

$$x=7$$

Whakakapia te 7 mō te x me te 1 mō z i te whārite y=2x+5z-16.

$$y=2\times 7+5\times 1-16$$

Tātaitia te y i te y=2\times 7+5\times 1-16.

$$y=3$$

Kua oti te pūnaha te whakatau.

$$x=7 y=3 z=1$$