Whakaoti i te {l}{3x+5y+6z=24}{5x+7y+3z=150}{x+y+z=-8}

$$\left. \begin{array} { l } { 3 x + 5 y + 6 z = 24 } \\ { 5 x + 7 y + 3 z = 150 } \\ { x + y + z = - 8 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x = -\frac{231}{5} = -46\frac{1}{5} = -46.2$$

$$y = \frac{333}{5} = 66\frac{3}{5} = 66.6$$

$$z = -\frac{142}{5} = -28\frac{2}{5} = -28.4$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me raupapa anō ngā whārite.

$$x+y+z=-8 5x+7y+3z=150 3x+5y+6z=24$$

Me whakaoti te x+y+z=-8 mō x.

$$x=-y-z-8$$

Whakakapia te -y-z-8 mō te x i te whārite tuarua me te tuatoru.

$$5\left(-y-z-8\right)+7y+3z=150 3\left(-y-z-8\right)+5y+6z=24$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=95+z z=16-\frac{2}{3}y$$

Whakakapia te 95+z mō te y i te whārite z=16-\frac{2}{3}y.

$$z=16-\frac{2}{3}\left(95+z\right)$$

Me whakaoti te z=16-\frac{2}{3}\left(95+z\right) mō z.

$$z=-\frac{142}{5}$$

Whakakapia te -\frac{142}{5} mō te z i te whārite y=95+z.

$$y=95-\frac{142}{5}$$

Tātaitia te y i te y=95-\frac{142}{5}.

$$y=\frac{333}{5}$$

Whakakapia te \frac{333}{5} mō te y me te -\frac{142}{5} mō z i te whārite x=-y-z-8.

$$x=-\frac{333}{5}-\left(-\frac{142}{5}\right)-8$$

Tātaitia te x i te x=-\frac{333}{5}-\left(-\frac{142}{5}\right)-8.

$$x=-\frac{231}{5}$$

Kua oti te pūnaha te whakatau.

$$x=-\frac{231}{5} y=\frac{333}{5} z=-\frac{142}{5}$$