Whakaoti i te {l}{4x+7y+8z=143}{6x+y+z=52}{3x+5y+4z=91}

$$\left\{ \begin{array}{l}{ 4 x + 7 y + 8 z = 143 }\\{ 6 x + y + z = 52 }\\{ 3 x + 5 y + 4 z = 91 }\end{array} \right.$$

Whakaoti mō x, y, z

$$x=6$$

$$y=9$$

$$z=7$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me raupapa anō ngā whārite.

$$6x+y+z=52 4x+7y+8z=143 3x+5y+4z=91$$

Me whakaoti te 6x+y+z=52 mō y.

$$y=-6x-z+52$$

Whakakapia te -6x-z+52 mō te y i te whārite tuarua me te tuatoru.

$$4x+7\left(-6x-z+52\right)+8z=143 3x+5\left(-6x-z+52\right)+4z=91$$

Me whakaoti ēnei whārite mō x me z takitahi.

$$x=\frac{221}{38}+\frac{1}{38}z z=-27x+169$$

Whakakapia te \frac{221}{38}+\frac{1}{38}z mō te x i te whārite z=-27x+169.

$$z=-27\left(\frac{221}{38}+\frac{1}{38}z\right)+169$$

Me whakaoti te z=-27\left(\frac{221}{38}+\frac{1}{38}z\right)+169 mō z.

$$z=7$$

Whakakapia te 7 mō te z i te whārite x=\frac{221}{38}+\frac{1}{38}z.

$$x=\frac{221}{38}+\frac{1}{38}\times 7$$

Tātaitia te x i te x=\frac{221}{38}+\frac{1}{38}\times 7.

$$x=6$$

Whakakapia te 6 mō te x me te 7 mō z i te whārite y=-6x-z+52.

$$y=-6\times 6-7+52$$

Tātaitia te y i te y=-6\times 6-7+52.

$$y=9$$

Kua oti te pūnaha te whakatau.

$$x=6 y=9 z=7$$