Whakaoti i te {l}{x+y+z=0}{2x-y-z=2}{x-z=3}

$$\left. \begin{array} { l } { x + y + z = 0 } \\ { 2 x - y - z = 2 } \\ { x - z = 3 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=\frac{2}{3}\approx 0.666666667$$

$$y = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

$$z = -\frac{7}{3} = -2\frac{1}{3} \approx -2.333333333$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te x+y+z=0 mō x.

$$x=-y-z$$

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

$$2\left(-y-z\right)-y-z=2 -y-z-z=3$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=-z-\frac{2}{3} z=-\frac{3}{2}-\frac{1}{2}y$$

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

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

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

$$z=-\frac{7}{3}$$

Whakakapia te -\frac{7}{3} mō te z i te whārite y=-z-\frac{2}{3}.

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

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

$$y=\frac{5}{3}$$

Whakakapia te \frac{5}{3} mō te y me te -\frac{7}{3} mō z i te whārite x=-y-z.

$$x=-\frac{5}{3}-\left(-\frac{7}{3}\right)$$

Tātaitia te x i te x=-\frac{5}{3}-\left(-\frac{7}{3}\right).

$$x=\frac{2}{3}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{2}{3} y=\frac{5}{3} z=-\frac{7}{3}$$