Whakaoti i te {l}{3x+2y+2z=3}{x+2y-z=5}{2x-4y+z=0}

$$\left. \begin{array} { l } { 3 x + 2 y + 2 z = 3 } \\ { x + 2 y - z = 5 } \\ { 2 x - 4 y + z = 0 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=2$$

$$y=\frac{1}{2}=0.5$$

$$z=-2$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me raupapa anō ngā whārite.

$$x+2y-z=5 3x+2y+2z=3 2x-4y+z=0$$

Me whakaoti te x+2y-z=5 mō x.

$$x=-2y+z+5$$

Whakakapia te -2y+z+5 mō te x i te whārite tuarua me te tuatoru.

$$3\left(-2y+z+5\right)+2y+2z=3 2\left(-2y+z+5\right)-4y+z=0$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=\frac{5}{4}z+3 z=-\frac{10}{3}+\frac{8}{3}y$$

Whakakapia te \frac{5}{4}z+3 mō te y i te whārite z=-\frac{10}{3}+\frac{8}{3}y.

$$z=-\frac{10}{3}+\frac{8}{3}\left(\frac{5}{4}z+3\right)$$

Me whakaoti te z=-\frac{10}{3}+\frac{8}{3}\left(\frac{5}{4}z+3\right) mō z.

$$z=-2$$

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

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

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

$$y=\frac{1}{2}$$

Whakakapia te \frac{1}{2} mō te y me te -2 mō z i te whārite x=-2y+z+5.

$$x=-2\times \frac{1}{2}-2+5$$

Tātaitia te x i te x=-2\times \frac{1}{2}-2+5.

$$x=2$$

Kua oti te pūnaha te whakatau.

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