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

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

Whakaoti mō x, y, z

$$x=3$$

$$y=-1$$

$$z=2$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Whakakapia te y+2z mō te x i te whārite 3x-z=7.

$$3\left(y+2z\right)-z=7$$

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

$$y=\frac{7}{3}-\frac{5}{3}z z=\frac{7}{3}+\frac{1}{3}y$$

Whakakapia te \frac{7}{3}-\frac{5}{3}z mō te y i te whārite z=\frac{7}{3}+\frac{1}{3}y.

$$z=\frac{7}{3}+\frac{1}{3}\left(\frac{7}{3}-\frac{5}{3}z\right)$$

Me whakaoti te z=\frac{7}{3}+\frac{1}{3}\left(\frac{7}{3}-\frac{5}{3}z\right) mō z.

$$z=2$$

Whakakapia te 2 mō te z i te whārite y=\frac{7}{3}-\frac{5}{3}z.

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

Tātaitia te y i te y=\frac{7}{3}-\frac{5}{3}\times 2.

$$y=-1$$

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

$$x=-1+2\times 2$$

Tātaitia te x i te x=-1+2\times 2.

$$x=3$$

Kua oti te pūnaha te whakatau.

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