Whakaoti i te {c}{x+y-3z=-36}{2x-y+6z=78}{x-2y+5z=42}

$$\left. \begin{array} { c } { x + y - 3 z = - 36 } \\ { 2 x - y + 6 z = 78 } \\ { x - 2 y + 5 z = 42 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=-4$$

$$y=22$$

$$z=18$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te x+y-3z=-36 mō x.

$$x=-y+3z-36$$

Whakakapia te -y+3z-36 mō te x i te whārite tuarua me te tuatoru.

$$2\left(-y+3z-36\right)-y+6z=78 -y+3z-36-2y+5z=42$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=-50+4z z=\frac{39}{4}+\frac{3}{8}y$$

Whakakapia te -50+4z mō te y i te whārite z=\frac{39}{4}+\frac{3}{8}y.

$$z=\frac{39}{4}+\frac{3}{8}\left(-50+4z\right)$$

Me whakaoti te z=\frac{39}{4}+\frac{3}{8}\left(-50+4z\right) mō z.

$$z=18$$

Whakakapia te 18 mō te z i te whārite y=-50+4z.

$$y=-50+4\times 18$$

Tātaitia te y i te y=-50+4\times 18.

$$y=22$$

Whakakapia te 22 mō te y me te 18 mō z i te whārite x=-y+3z-36.

$$x=-22+3\times 18-36$$

Tātaitia te x i te x=-22+3\times 18-36.

$$x=-4$$

Kua oti te pūnaha te whakatau.

$$x=-4 y=22 z=18$$