Whakaoti i te {c}{x+2y+3z=1}{5x+3y+20z=0}{3x+4y+8z=3}

$$\left\{ \begin{array} { c } { x + 2 y + 3 z = 1 } \\ { 5 x + 3 y + 20 z = 0 } \\ { 3 x + 4 y + 8 z = 3 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x = \frac{37}{17} = 2\frac{3}{17} \approx 2.176470588$$

$$y=\frac{5}{17}\approx 0.294117647$$

$$z=-\frac{10}{17}\approx -0.588235294$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te x+2y+3z=1 mō x.

$$x=-2y-3z+1$$

Whakakapia te -2y-3z+1 mō te x i te whārite tuarua me te tuatoru.

$$5\left(-2y-3z+1\right)+3y+20z=0 3\left(-2y-3z+1\right)+4y+8z=3$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=\frac{5}{7}+\frac{5}{7}z z=-2y$$

Whakakapia te \frac{5}{7}+\frac{5}{7}z mō te y i te whārite z=-2y.

$$z=-2\left(\frac{5}{7}+\frac{5}{7}z\right)$$

Me whakaoti te z=-2\left(\frac{5}{7}+\frac{5}{7}z\right) mō z.

$$z=-\frac{10}{17}$$

Whakakapia te -\frac{10}{17} mō te z i te whārite y=\frac{5}{7}+\frac{5}{7}z.

$$y=\frac{5}{7}+\frac{5}{7}\left(-\frac{10}{17}\right)$$

Tātaitia te y i te y=\frac{5}{7}+\frac{5}{7}\left(-\frac{10}{17}\right).

$$y=\frac{5}{17}$$

Whakakapia te \frac{5}{17} mō te y me te -\frac{10}{17} mō z i te whārite x=-2y-3z+1.

$$x=-2\times \frac{5}{17}-3\left(-\frac{10}{17}\right)+1$$

Tātaitia te x i te x=-2\times \frac{5}{17}-3\left(-\frac{10}{17}\right)+1.

$$x=\frac{37}{17}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{37}{17} y=\frac{5}{17} z=-\frac{10}{17}$$