Whakaoti i te {l}{x+y+z=3}{3x+2y-z=10}{2x-5y-z=-5}

$$\left. \begin{array} { l } { x + y + z = 3 } \\ { 3 x + 2 y - z = 10 } \\ { 2 x - 5 y - z = - 5 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x = \frac{46}{25} = 1\frac{21}{25} = 1.84$$

$$y = \frac{47}{25} = 1\frac{22}{25} = 1.88$$

$$z=-\frac{18}{25}=-0.72$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te x+y+z=3 mō x.

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

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

$$3\left(-y-z+3\right)+2y-z=10 2\left(-y-z+3\right)-5y-z=-5$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=-4z-1 z=-\frac{7}{3}y+\frac{11}{3}$$

Whakakapia te -4z-1 mō te y i te whārite z=-\frac{7}{3}y+\frac{11}{3}.

$$z=-\frac{7}{3}\left(-4z-1\right)+\frac{11}{3}$$

Me whakaoti te z=-\frac{7}{3}\left(-4z-1\right)+\frac{11}{3} mō z.

$$z=-\frac{18}{25}$$

Whakakapia te -\frac{18}{25} mō te z i te whārite y=-4z-1.

$$y=-4\left(-\frac{18}{25}\right)-1$$

Tātaitia te y i te y=-4\left(-\frac{18}{25}\right)-1.

$$y=\frac{47}{25}$$

Whakakapia te \frac{47}{25} mō te y me te -\frac{18}{25} mō z i te whārite x=-y-z+3.

$$x=-\frac{47}{25}-\left(-\frac{18}{25}\right)+3$$

Tātaitia te x i te x=-\frac{47}{25}-\left(-\frac{18}{25}\right)+3.

$$x=\frac{46}{25}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{46}{25} y=\frac{47}{25} z=-\frac{18}{25}$$