Whakaoti i te {l}{x+2y+62=05quad(1)}{-x+y-2z=3}{x-4y-2z=1}

$$\left\{ \begin{array} { l } { x + 2 y + 62 = 05 \quad ( 1 ) } \\ { - x + y - 2 z = 3 } \\ { x - 4 y - 2 z = 1 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x = -\frac{289}{9} = -32\frac{1}{9} \approx -32.111111111$$

$$y = -\frac{112}{9} = -12\frac{4}{9} \approx -12.444444444$$

$$z = \frac{25}{3} = 8\frac{1}{3} \approx 8.333333333$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te x+2y+62=5\times 1 mō x.

$$x=-2y-57$$

Whakakapia te -2y-57 mō te x i te whārite tuarua me te tuatoru.

$$-\left(-2y-57\right)+y-2z=3 -2y-57-4y-2z=1$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=-18+\frac{2}{3}z z=-29-3y$$

Whakakapia te -18+\frac{2}{3}z mō te y i te whārite z=-29-3y.

$$z=-29-3\left(-18+\frac{2}{3}z\right)$$

Me whakaoti te z=-29-3\left(-18+\frac{2}{3}z\right) mō z.

$$z=\frac{25}{3}$$

Whakakapia te \frac{25}{3} mō te z i te whārite y=-18+\frac{2}{3}z.

$$y=-18+\frac{2}{3}\times \frac{25}{3}$$

Tātaitia te y i te y=-18+\frac{2}{3}\times \frac{25}{3}.

$$y=-\frac{112}{9}$$

Whakakapia te -\frac{112}{9} mō te y i te whārite x=-2y-57.

$$x=-2\left(-\frac{112}{9}\right)-57$$

Tātaitia te x i te x=-2\left(-\frac{112}{9}\right)-57.

$$x=-\frac{289}{9}$$

Kua oti te pūnaha te whakatau.

$$x=-\frac{289}{9} y=-\frac{112}{9} z=\frac{25}{3}$$