Whakaoti i te {l}{2x+4y-12z=6}{x+y+2z=26}{3x-3y+3z=30}

$$\left. \begin{array} { l } { 2 x + 4 y - 12 z = 6 } \\ { x + y + 2 z = 26 } \\ { 3 x - 3 y + 3 z = 30 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x = \frac{213}{17} = 12\frac{9}{17} \approx 12.529411765$$

$$y = \frac{105}{17} = 6\frac{3}{17} \approx 6.176470588$$

$$z = \frac{62}{17} = 3\frac{11}{17} \approx 3.647058824$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me raupapa anō ngā whārite.

$$x+y+2z=26 2x+4y-12z=6 3x-3y+3z=30$$

Me whakaoti te x+y+2z=26 mō x.

$$x=-y-2z+26$$

Whakakapia te -y-2z+26 mō te x i te whārite tuarua me te tuatoru.

$$2\left(-y-2z+26\right)+4y-12z=6 3\left(-y-2z+26\right)-3y+3z=30$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=-23+8z z=16-2y$$

Whakakapia te -23+8z mō te y i te whārite z=16-2y.

$$z=16-2\left(-23+8z\right)$$

Me whakaoti te z=16-2\left(-23+8z\right) mō z.

$$z=\frac{62}{17}$$

Whakakapia te \frac{62}{17} mō te z i te whārite y=-23+8z.

$$y=-23+8\times \frac{62}{17}$$

Tātaitia te y i te y=-23+8\times \frac{62}{17}.

$$y=\frac{105}{17}$$

Whakakapia te \frac{105}{17} mō te y me te \frac{62}{17} mō z i te whārite x=-y-2z+26.

$$x=-\frac{105}{17}-2\times \frac{62}{17}+26$$

Tātaitia te x i te x=-\frac{105}{17}-2\times \frac{62}{17}+26.

$$x=\frac{213}{17}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{213}{17} y=\frac{105}{17} z=\frac{62}{17}$$