Whakaoti i te {r}{4x-3y+z=-20}{-2x+y-3z=-8}{x-y+2z=7}

$$\left\{ \begin{array} { r } { 4 x - 3 y + z = - 20 } \\ { - 2 x + y - 3 z = - 8 } \\ { x - y + 2 z = 7 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=-6$$

$$y=1$$

$$z=7$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te 4x-3y+z=-20 mō z.

$$z=-4x+3y-20$$

Whakakapia te -4x+3y-20 mō te z i te whārite tuarua me te tuatoru.

$$-2x+y-3\left(-4x+3y-20\right)=-8 x-y+2\left(-4x+3y-20\right)=7$$

Me whakaoti ēnei whārite mō y me x takitahi.

$$y=\frac{17}{2}+\frac{5}{4}x x=\frac{5}{7}y-\frac{47}{7}$$

Whakakapia te \frac{17}{2}+\frac{5}{4}x mō te y i te whārite x=\frac{5}{7}y-\frac{47}{7}.

$$x=\frac{5}{7}\left(\frac{17}{2}+\frac{5}{4}x\right)-\frac{47}{7}$$

Me whakaoti te x=\frac{5}{7}\left(\frac{17}{2}+\frac{5}{4}x\right)-\frac{47}{7} mō x.

$$x=-6$$

Whakakapia te -6 mō te x i te whārite y=\frac{17}{2}+\frac{5}{4}x.

$$y=\frac{17}{2}+\frac{5}{4}\left(-6\right)$$

Tātaitia te y i te y=\frac{17}{2}+\frac{5}{4}\left(-6\right).

$$y=1$$

Whakakapia te 1 mō te y me te -6 mō x i te whārite z=-4x+3y-20.

$$z=-4\left(-6\right)+3\times 1-20$$

Tātaitia te z i te z=-4\left(-6\right)+3\times 1-20.

$$z=7$$

Kua oti te pūnaha te whakatau.

$$x=-6 y=1 z=7$$