Whakaoti i te {l}{3x+5y-z=4}{10y-6x-3z=1}{4z-15y+9x=-1}

$$\left\{ \begin{array} { l } { 3 x + 5 y - z = 4 } \\ { 10 y - 6 x - 3 z = 1 } \\ { 4 z - 15 y + 9 x = - 1 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=\frac{2}{3}\approx 0.666666667$$

$$y=\frac{1}{5}=0.2$$

$$z=-1$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te 3x+5y-z=4 mō z.

$$z=3x+5y-4$$

Whakakapia te 3x+5y-4 mō te z i te whārite tuarua me te tuatoru.

$$10y-6x-3\left(3x+5y-4\right)=1 4\left(3x+5y-4\right)-15y+9x=-1$$

Me whakaoti ēnei whārite mō y me x takitahi.

$$y=-3x+\frac{11}{5} x=\frac{5}{7}-\frac{5}{21}y$$

Whakakapia te -3x+\frac{11}{5} mō te y i te whārite x=\frac{5}{7}-\frac{5}{21}y.

$$x=\frac{5}{7}-\frac{5}{21}\left(-3x+\frac{11}{5}\right)$$

Me whakaoti te x=\frac{5}{7}-\frac{5}{21}\left(-3x+\frac{11}{5}\right) mō x.

$$x=\frac{2}{3}$$

Whakakapia te \frac{2}{3} mō te x i te whārite y=-3x+\frac{11}{5}.

$$y=-3\times \frac{2}{3}+\frac{11}{5}$$

Tātaitia te y i te y=-3\times \frac{2}{3}+\frac{11}{5}.

$$y=\frac{1}{5}$$

Whakakapia te \frac{1}{5} mō te y me te \frac{2}{3} mō x i te whārite z=3x+5y-4.

$$z=3\times \frac{2}{3}+5\times \frac{1}{5}-4$$

Tātaitia te z i te z=3\times \frac{2}{3}+5\times \frac{1}{5}-4.

$$z=-1$$

Kua oti te pūnaha te whakatau.

$$x=\frac{2}{3} y=\frac{1}{5} z=-1$$