Whakaoti i te {l}{4x+2y-2z=-8}{-6x+4y+2z=0}{2x+2y+12z=60}

$$\left\{ \begin{array} { l } { 4 x + 2 y - 2 z = - 8 } \\ { - 6 x + 4 y + 2 z = 0 } \\ { 2 x + 2 y + 12 z = 60 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=1$$

$$y=-1$$

$$z=5$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te 4x+2y-2z=-8 mō x.

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

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

$$-6\left(-2-\frac{1}{2}y+\frac{1}{2}z\right)+4y+2z=0 2\left(-2-\frac{1}{2}y+\frac{1}{2}z\right)+2y+12z=60$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=-\frac{12}{7}+\frac{1}{7}z z=\frac{64}{13}-\frac{1}{13}y$$

Whakakapia te -\frac{12}{7}+\frac{1}{7}z mō te y i te whārite z=\frac{64}{13}-\frac{1}{13}y.

$$z=\frac{64}{13}-\frac{1}{13}\left(-\frac{12}{7}+\frac{1}{7}z\right)$$

Me whakaoti te z=\frac{64}{13}-\frac{1}{13}\left(-\frac{12}{7}+\frac{1}{7}z\right) mō z.

$$z=5$$

Whakakapia te 5 mō te z i te whārite y=-\frac{12}{7}+\frac{1}{7}z.

$$y=-\frac{12}{7}+\frac{1}{7}\times 5$$

Tātaitia te y i te y=-\frac{12}{7}+\frac{1}{7}\times 5.

$$y=-1$$

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

$$x=-2-\frac{1}{2}\left(-1\right)+\frac{1}{2}\times 5$$

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

$$x=1$$

Kua oti te pūnaha te whakatau.

$$x=1 y=-1 z=5$$