Whakaoti i te {c}{2x+3y=1}{4x-3y+z=-2}{x-y+z=1}

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

Whakaoti mō x, y, z

$$x=-\frac{7}{13}\approx -0.538461538$$

$$y=\frac{9}{13}\approx 0.692307692$$

$$z = \frac{29}{13} = 2\frac{3}{13} \approx 2.230769231$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me raupapa anō ngā whārite.

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

Me whakaoti te 4x-3y+z=-2 mō z.

$$z=-4x+3y-2$$

Whakakapia te -4x+3y-2 mō te z i te whārite x-y+z=1.

$$x-y-4x+3y-2=1$$

Me whakaoti te whārite tuarua mō y me te whārite tuatoru mō x.

$$y=-\frac{2}{3}x+\frac{1}{3} x=\frac{2}{3}y-1$$

Whakakapia te -\frac{2}{3}x+\frac{1}{3} mō te y i te whārite x=\frac{2}{3}y-1.

$$x=\frac{2}{3}\left(-\frac{2}{3}x+\frac{1}{3}\right)-1$$

Me whakaoti te x=\frac{2}{3}\left(-\frac{2}{3}x+\frac{1}{3}\right)-1 mō x.

$$x=-\frac{7}{13}$$

Whakakapia te -\frac{7}{13} mō te x i te whārite y=-\frac{2}{3}x+\frac{1}{3}.

$$y=-\frac{2}{3}\left(-\frac{7}{13}\right)+\frac{1}{3}$$

Tātaitia te y i te y=-\frac{2}{3}\left(-\frac{7}{13}\right)+\frac{1}{3}.

$$y=\frac{9}{13}$$

Whakakapia te \frac{9}{13} mō te y me te -\frac{7}{13} mō x i te whārite z=-4x+3y-2.

$$z=-4\left(-\frac{7}{13}\right)+3\times \frac{9}{13}-2$$

Tātaitia te z i te z=-4\left(-\frac{7}{13}\right)+3\times \frac{9}{13}-2.

$$z=\frac{29}{13}$$

Kua oti te pūnaha te whakatau.

$$x=-\frac{7}{13} y=\frac{9}{13} z=\frac{29}{13}$$