Whakaoti i te {l}{x+y-4z=0}{4x+7z=41}{4x+3y=41}

$$\left\{ \begin{array}{l}{ x + y - 4 z = 0 }\\{ 4 x + 7 z = 41 }\\{ 4 x + 3 y = 41 }\end{array} \right.$$

Whakaoti mō x, y, z

$$x=5$$

$$y=7$$

$$z=3$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te x+y-4z=0 mō x.

$$x=-y+4z$$

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

$$4\left(-y+4z\right)+7z=41 4\left(-y+4z\right)+3y=41$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=-\frac{41}{4}+\frac{23}{4}z z=\frac{41}{16}+\frac{1}{16}y$$

Whakakapia te -\frac{41}{4}+\frac{23}{4}z mō te y i te whārite z=\frac{41}{16}+\frac{1}{16}y.

$$z=\frac{41}{16}+\frac{1}{16}\left(-\frac{41}{4}+\frac{23}{4}z\right)$$

Me whakaoti te z=\frac{41}{16}+\frac{1}{16}\left(-\frac{41}{4}+\frac{23}{4}z\right) mō z.

$$z=3$$

Whakakapia te 3 mō te z i te whārite y=-\frac{41}{4}+\frac{23}{4}z.

$$y=-\frac{41}{4}+\frac{23}{4}\times 3$$

Tātaitia te y i te y=-\frac{41}{4}+\frac{23}{4}\times 3.

$$y=7$$

Whakakapia te 7 mō te y me te 3 mō z i te whārite x=-y+4z.

$$x=-7+4\times 3$$

Tātaitia te x i te x=-7+4\times 3.

$$x=5$$

Kua oti te pūnaha te whakatau.

$$x=5 y=7 z=3$$