Whakaoti i te {l}{3x+2y+z=5}{x+y+5z=3}{x-y+2z=-2}

$$\left. \begin{array} { l } { 3 x + 2 y + z = 5 } \\ { x + y + 5 z = 3 } \\ { x - y + 2 z = - 2 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=\frac{2}{25}=0.08$$

$$y = \frac{58}{25} = 2\frac{8}{25} = 2.32$$

$$z=\frac{3}{25}=0.12$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te 3x+2y+z=5 mō z.

$$z=-3x-2y+5$$

Whakakapia te -3x-2y+5 mō te z i te whārite tuarua me te tuatoru.

$$x+y+5\left(-3x-2y+5\right)=3 x-y+2\left(-3x-2y+5\right)=-2$$

Me whakaoti ēnei whārite mō y me x takitahi.

$$y=\frac{22}{9}-\frac{14}{9}x x=-y+\frac{12}{5}$$

Whakakapia te \frac{22}{9}-\frac{14}{9}x mō te y i te whārite x=-y+\frac{12}{5}.

$$x=-\left(\frac{22}{9}-\frac{14}{9}x\right)+\frac{12}{5}$$

Me whakaoti te x=-\left(\frac{22}{9}-\frac{14}{9}x\right)+\frac{12}{5} mō x.

$$x=\frac{2}{25}$$

Whakakapia te \frac{2}{25} mō te x i te whārite y=\frac{22}{9}-\frac{14}{9}x.

$$y=\frac{22}{9}-\frac{14}{9}\times \frac{2}{25}$$

Tātaitia te y i te y=\frac{22}{9}-\frac{14}{9}\times \frac{2}{25}.

$$y=\frac{58}{25}$$

Whakakapia te \frac{58}{25} mō te y me te \frac{2}{25} mō x i te whārite z=-3x-2y+5.

$$z=-3\times \frac{2}{25}-2\times \frac{58}{25}+5$$

Tātaitia te z i te z=-3\times \frac{2}{25}-2\times \frac{58}{25}+5.

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

Kua oti te pūnaha te whakatau.

$$x=\frac{2}{25} y=\frac{58}{25} z=\frac{3}{25}$$