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

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

Whakaoti mō x, y, z

$$x=-\frac{5}{11}\approx -0.454545455$$

$$y = -\frac{13}{11} = -1\frac{2}{11} \approx -1.181818182$$

$$z=\frac{3}{11}\approx 0.272727273$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me raupapa anō ngā whārite.

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

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.

$$y=-\frac{1}{3}x-\frac{4}{3} x=\frac{2}{3}y+\frac{1}{3}$$

Whakakapia te -\frac{1}{3}x-\frac{4}{3} mō te y i te whārite x=\frac{2}{3}y+\frac{1}{3}.

$$x=\frac{2}{3}\left(-\frac{1}{3}x-\frac{4}{3}\right)+\frac{1}{3}$$

Me whakaoti te x=\frac{2}{3}\left(-\frac{1}{3}x-\frac{4}{3}\right)+\frac{1}{3} mō x.

$$x=-\frac{5}{11}$$

Whakakapia te -\frac{5}{11} mō te x i te whārite y=-\frac{1}{3}x-\frac{4}{3}.

$$y=-\frac{1}{3}\left(-\frac{5}{11}\right)-\frac{4}{3}$$

Tātaitia te y i te y=-\frac{1}{3}\left(-\frac{5}{11}\right)-\frac{4}{3}.

$$y=-\frac{13}{11}$$

Whakakapia te -\frac{13}{11} mō te y me te -\frac{5}{11} mō x i te whārite z=-4x+3y+2.

$$z=-4\left(-\frac{5}{11}\right)+3\left(-\frac{13}{11}\right)+2$$

Tātaitia te z i te z=-4\left(-\frac{5}{11}\right)+3\left(-\frac{13}{11}\right)+2.

$$z=\frac{3}{11}$$

Kua oti te pūnaha te whakatau.

$$x=-\frac{5}{11} y=-\frac{13}{11} z=\frac{3}{11}$$