Whakaoti i te {l}{5x-2y+2=4}{x-y-4z=1}{2x-4y+2z=8}

$$\left. \begin{array} { l } { 5 x - 2 y + 2 = 4 } \\ { x - y - 4 z = 1 } \\ { 2 x - 4 y + 2 z = 8 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=-\frac{16}{35}\approx -0.457142857$$

$$y = -\frac{15}{7} = -2\frac{1}{7} \approx -2.142857143$$

$$z=\frac{6}{35}\approx 0.171428571$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me raupapa anō ngā whārite.

$$x-y-4z=1 5x-2y+2=4 2x-4y+2z=8$$

Me whakaoti te x-y-4z=1 mō x.

$$x=y+4z+1$$

Whakakapia te y+4z+1 mō te x i te whārite tuarua me te tuatoru.

$$5\left(y+4z+1\right)-2y+2=4 2\left(y+4z+1\right)-4y+2z=8$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=-\frac{20}{3}z-1 z=\frac{3}{5}+\frac{1}{5}y$$

Whakakapia te -\frac{20}{3}z-1 mō te y i te whārite z=\frac{3}{5}+\frac{1}{5}y.

$$z=\frac{3}{5}+\frac{1}{5}\left(-\frac{20}{3}z-1\right)$$

Me whakaoti te z=\frac{3}{5}+\frac{1}{5}\left(-\frac{20}{3}z-1\right) mō z.

$$z=\frac{6}{35}$$

Whakakapia te \frac{6}{35} mō te z i te whārite y=-\frac{20}{3}z-1.

$$y=-\frac{20}{3}\times \frac{6}{35}-1$$

Tātaitia te y i te y=-\frac{20}{3}\times \frac{6}{35}-1.

$$y=-\frac{15}{7}$$

Whakakapia te -\frac{15}{7} mō te y me te \frac{6}{35} mō z i te whārite x=y+4z+1.

$$x=-\frac{15}{7}+4\times \frac{6}{35}+1$$

Tātaitia te x i te x=-\frac{15}{7}+4\times \frac{6}{35}+1.

$$x=-\frac{16}{35}$$

Kua oti te pūnaha te whakatau.

$$x=-\frac{16}{35} y=-\frac{15}{7} z=\frac{6}{35}$$