Whakaoti i te {l}{x+y-2y=-3}{5x-2y+7z=22}{2x-5y+4z=4}

$$\left. \begin{array} { l } { x + y - 2 y = - 3 } \\ { 5 x - 2 y + 7 z = 22 } \\ { 2 x - 5 y + 4 z = 4 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=-\frac{7}{11}\approx -0.636363636$$

$$y = \frac{26}{11} = 2\frac{4}{11} \approx 2.363636364$$

$$z = \frac{47}{11} = 4\frac{3}{11} \approx 4.272727273$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te x+y-2y=-3 mō x.

$$x=y-3$$

Whakakapia te y-3 mō te x i te whārite tuarua me te tuatoru.

$$5\left(y-3\right)-2y+7z=22 2\left(y-3\right)-5y+4z=4$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=\frac{37}{3}-\frac{7}{3}z z=\frac{3}{4}y+\frac{5}{2}$$

Whakakapia te \frac{37}{3}-\frac{7}{3}z mō te y i te whārite z=\frac{3}{4}y+\frac{5}{2}.

$$z=\frac{3}{4}\left(\frac{37}{3}-\frac{7}{3}z\right)+\frac{5}{2}$$

Me whakaoti te z=\frac{3}{4}\left(\frac{37}{3}-\frac{7}{3}z\right)+\frac{5}{2} mō z.

$$z=\frac{47}{11}$$

Whakakapia te \frac{47}{11} mō te z i te whārite y=\frac{37}{3}-\frac{7}{3}z.

$$y=\frac{37}{3}-\frac{7}{3}\times \frac{47}{11}$$

Tātaitia te y i te y=\frac{37}{3}-\frac{7}{3}\times \frac{47}{11}.

$$y=\frac{26}{11}$$

Whakakapia te \frac{26}{11} mō te y i te whārite x=y-3.

$$x=\frac{26}{11}-3$$

Tātaitia te x i te x=\frac{26}{11}-3.

$$x=-\frac{7}{11}$$

Kua oti te pūnaha te whakatau.

$$x=-\frac{7}{11} y=\frac{26}{11} z=\frac{47}{11}$$