Whakaoti i te {l}{5x-3y+2z=20}{4x+6y-5z=-2}{8x+y-z=21}

$$\left. \begin{array} { l } { 5 x - 3 y + 2 z = 20 } \\ { 4 x + 6 y - 5 z = - 2 } \\ { 8 x + y - z = 21 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=3$$

$$y=1$$

$$z=4$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me raupapa anō ngā whārite.

$$8x+y-z=21 4x+6y-5z=-2 5x-3y+2z=20$$

Me whakaoti te 8x+y-z=21 mō y.

$$y=-8x+z+21$$

Whakakapia te -8x+z+21 mō te y i te whārite tuarua me te tuatoru.

$$4x+6\left(-8x+z+21\right)-5z=-2 5x-3\left(-8x+z+21\right)+2z=20$$

Me whakaoti ēnei whārite mō x me z takitahi.

$$x=\frac{32}{11}+\frac{1}{44}z z=29x-83$$

Whakakapia te \frac{32}{11}+\frac{1}{44}z mō te x i te whārite z=29x-83.

$$z=29\left(\frac{32}{11}+\frac{1}{44}z\right)-83$$

Me whakaoti te z=29\left(\frac{32}{11}+\frac{1}{44}z\right)-83 mō z.

$$z=4$$

Whakakapia te 4 mō te z i te whārite x=\frac{32}{11}+\frac{1}{44}z.

$$x=\frac{32}{11}+\frac{1}{44}\times 4$$

Tātaitia te x i te x=\frac{32}{11}+\frac{1}{44}\times 4.

$$x=3$$

Whakakapia te 3 mō te x me te 4 mō z i te whārite y=-8x+z+21.

$$y=-8\times 3+4+21$$

Tātaitia te y i te y=-8\times 3+4+21.

$$y=1$$

Kua oti te pūnaha te whakatau.

$$x=3 y=1 z=4$$