Whakaoti i te {c}{x+y+z=15000}{9x+6y+5z=89000}{4.5x+6y+2.5z=50500}

$$\left. \begin{array} { c } { x + y + z = 15000 } \\ { 9 x + 6 y + 5 z = 89000 } \\ { 4.5 x + 6 y + 2.5 z = 50500 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=3000$$

$$y=2000$$

$$z=10000$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te x+y+z=15000 mō x.

$$x=-y-z+15000$$

Whakakapia te -y-z+15000 mō te x i te whārite tuarua me te tuatoru.

$$9\left(-y-z+15000\right)+6y+5z=89000 4.5\left(-y-z+15000\right)+6y+2.5z=50500$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=\frac{46000}{3}-\frac{4}{3}z z=\frac{3}{4}y+8500$$

Whakakapia te \frac{46000}{3}-\frac{4}{3}z mō te y i te whārite z=\frac{3}{4}y+8500.

$$z=\frac{3}{4}\left(\frac{46000}{3}-\frac{4}{3}z\right)+8500$$

Me whakaoti te z=\frac{3}{4}\left(\frac{46000}{3}-\frac{4}{3}z\right)+8500 mō z.

$$z=10000$$

Whakakapia te 10000 mō te z i te whārite y=\frac{46000}{3}-\frac{4}{3}z.

$$y=\frac{46000}{3}-\frac{4}{3}\times 10000$$

Tātaitia te y i te y=\frac{46000}{3}-\frac{4}{3}\times 10000.

$$y=2000$$

Whakakapia te 2000 mō te y me te 10000 mō z i te whārite x=-y-z+15000.

$$x=-2000-10000+15000$$

Tātaitia te x i te x=-2000-10000+15000.

$$x=3000$$

Kua oti te pūnaha te whakatau.

$$x=3000 y=2000 z=10000$$