Whakaoti i te {l}{5x+y-2z=4}{2x+y=1}{5x+3y-2z=6}

$$\left. \begin{array} { l } { 5 x + y - 2 z = 4 } \\ { 2 x + y = 1 } \\ { 5 x + 3 y - 2 z = 6 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=0$$

$$y=1$$

$$z = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te 5x+y-2z=4 mō y.

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

Whakakapia te -5x+2z+4 mō te y i te whārite tuarua me te tuatoru.

$$2x-5x+2z+4=1 5x+3\left(-5x+2z+4\right)-2z=6$$

Me whakaoti ēnei whārite mō x me z takitahi.

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

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

$$z=-\frac{3}{2}+\frac{5}{2}\left(\frac{2}{3}z+1\right)$$

Me whakaoti te z=-\frac{3}{2}+\frac{5}{2}\left(\frac{2}{3}z+1\right) mō z.

$$z=-\frac{3}{2}$$

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

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

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

$$x=0$$

Whakakapia te 0 mō te x me te -\frac{3}{2} mō z i te whārite y=-5x+2z+4.

$$y=-5\times 0+2\left(-\frac{3}{2}\right)+4$$

Tātaitia te y i te y=-5\times 0+2\left(-\frac{3}{2}\right)+4.

$$y=1$$

Kua oti te pūnaha te whakatau.

$$x=0 y=1 z=-\frac{3}{2}$$