Whakaoti i te {l}{0.27x+0.02y+0.02z=200}{0.17x+0.07y+0.8z=175}{x+y+z=1000}

$$\left. \begin{array}{l}{ 0.27 x + 0.02 y + 0.02 z = 200 }\\{ 0.17 x + 0.07 y + 0.8 z = 175 }\\{ x + y + z = 1000 }\end{array} \right.$$

Whakaoti mō x, y, z

$$x=720$$

$$y = \frac{17140}{73} = 234\frac{58}{73} \approx 234.794520548$$

$$z = \frac{3300}{73} = 45\frac{15}{73} \approx 45.205479452$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me raupapa anō ngā whārite.

$$x+y+z=1000 0.17x+0.07y+0.8z=175 0.27x+0.02y+0.02z=200$$

Me whakaoti te x+y+z=1000 mō x.

$$x=-y-z+1000$$

Whakakapia te -y-z+1000 mō te x i te whārite tuarua me te tuatoru.

$$0.17\left(-y-z+1000\right)+0.07y+0.8z=175 0.27\left(-y-z+1000\right)+0.02y+0.02z=200$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=6.3z-50 z=-y+280$$

Whakakapia te 6.3z-50 mō te y i te whārite z=-y+280.

$$z=-\left(6.3z-50\right)+280$$

Me whakaoti te z=-\left(6.3z-50\right)+280 mō z.

$$z=\frac{3300}{73}$$

Whakakapia te \frac{3300}{73} mō te z i te whārite y=6.3z-50.

$$y=6.3\times \frac{3300}{73}-50$$

Tātaitia te y i te y=6.3\times \frac{3300}{73}-50.

$$y=\frac{17140}{73}$$

Whakakapia te \frac{17140}{73} mō te y me te \frac{3300}{73} mō z i te whārite x=-y-z+1000.

$$x=-\frac{17140}{73}-\frac{3300}{73}+1000$$

Tātaitia te x i te x=-\frac{17140}{73}-\frac{3300}{73}+1000.

$$x=720$$

Kua oti te pūnaha te whakatau.

$$x=720 y=\frac{17140}{73} z=\frac{3300}{73}$$