Whakaoti i te {l}{2x+3y+2z=1}{5x+3y-2z=2}{4x-y+7z=3}

$$\left\{ \begin{array} { l } { 2 x + 3 y + 2 z = 1 } \\ { 5 x + 3 y - 2 z = 2 } \\ { 4 x - y + 7 z = 3 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=\frac{63}{125}=0.504$$

$$y=-\frac{11}{125}=-0.088$$

$$z=\frac{16}{125}=0.128$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me raupapa anō ngā whārite.

$$4x-y+7z=3 5x+3y-2z=2 2x+3y+2z=1$$

Me whakaoti te 4x-y+7z=3 mō y.

$$y=4x+7z-3$$

Whakakapia te 4x+7z-3 mō te y i te whārite tuarua me te tuatoru.

$$5x+3\left(4x+7z-3\right)-2z=2 2x+3\left(4x+7z-3\right)+2z=1$$

Me whakaoti ēnei whārite mō x me z takitahi.

$$x=-\frac{19}{17}z+\frac{11}{17} z=\frac{10}{23}-\frac{14}{23}x$$

Whakakapia te -\frac{19}{17}z+\frac{11}{17} mō te x i te whārite z=\frac{10}{23}-\frac{14}{23}x.

$$z=\frac{10}{23}-\frac{14}{23}\left(-\frac{19}{17}z+\frac{11}{17}\right)$$

Me whakaoti te z=\frac{10}{23}-\frac{14}{23}\left(-\frac{19}{17}z+\frac{11}{17}\right) mō z.

$$z=\frac{16}{125}$$

Whakakapia te \frac{16}{125} mō te z i te whārite x=-\frac{19}{17}z+\frac{11}{17}.

$$x=-\frac{19}{17}\times \frac{16}{125}+\frac{11}{17}$$

Tātaitia te x i te x=-\frac{19}{17}\times \frac{16}{125}+\frac{11}{17}.

$$x=\frac{63}{125}$$

Whakakapia te \frac{63}{125} mō te x me te \frac{16}{125} mō z i te whārite y=4x+7z-3.

$$y=4\times \frac{63}{125}+7\times \frac{16}{125}-3$$

Tātaitia te y i te y=4\times \frac{63}{125}+7\times \frac{16}{125}-3.

$$y=-\frac{11}{125}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{63}{125} y=-\frac{11}{125} z=\frac{16}{125}$$