Whakaoti i te {l}{x/3+y/2+z/4=2}{x/4+frac{y}{3}-frac{z}{2}=frac{1}{6}}{frac{x}{2}-frac{y}{4}+frac{z}{3}=frac{23}{6}}

$$\left. \begin{array} { l } { \frac { x } { 3 } + \frac { y } { 2 } + \frac { z } { 4 } = 2 } \\ { \frac { x } { 4 } + \frac { y } { 3 } - \frac { z } { 2 } = \frac { 1 } { 6 } } \\ { \frac { x } { 2 } - \frac { y } { 4 } + \frac { z } { 3 } = \frac { 23 } { 6 } } \end{array} \right.$$

Whakaoti mō x, y, z

$$x = \frac{2322}{395} = 5\frac{347}{395} \approx 5.878481013$$

$$y=-\frac{362}{395}\approx -0.916455696$$

$$z = \frac{788}{395} = 1\frac{393}{395} \approx 1.994936709$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakarea ia whārite mā te taurea pātahi iti rawa o ngā tauraro kei roto. Whakarūnātia.

$$4x+6y+3z=24 3x+4y-6z=2 6x-3y+4z=46$$

Me whakaoti te 4x+6y+3z=24 mō x.

$$x=6-\frac{3}{2}y-\frac{3}{4}z$$

Whakakapia te 6-\frac{3}{2}y-\frac{3}{4}z mō te x i te whārite tuarua me te tuatoru.

$$3\left(6-\frac{3}{2}y-\frac{3}{4}z\right)+4y-6z=2 6\left(6-\frac{3}{2}y-\frac{3}{4}z\right)-3y+4z=46$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=32-\frac{33}{2}z z=-20-24y$$

Whakakapia te 32-\frac{33}{2}z mō te y i te whārite z=-20-24y.

$$z=-20-24\left(32-\frac{33}{2}z\right)$$

Me whakaoti te z=-20-24\left(32-\frac{33}{2}z\right) mō z.

$$z=\frac{788}{395}$$

Whakakapia te \frac{788}{395} mō te z i te whārite y=32-\frac{33}{2}z.

$$y=32-\frac{33}{2}\times \frac{788}{395}$$

Tātaitia te y i te y=32-\frac{33}{2}\times \frac{788}{395}.

$$y=-\frac{362}{395}$$

Whakakapia te -\frac{362}{395} mō te y me te \frac{788}{395} mō z i te whārite x=6-\frac{3}{2}y-\frac{3}{4}z.

$$x=6-\frac{3}{2}\left(-\frac{362}{395}\right)-\frac{3}{4}\times \frac{788}{395}$$

Tātaitia te x i te x=6-\frac{3}{2}\left(-\frac{362}{395}\right)-\frac{3}{4}\times \frac{788}{395}.

$$x=\frac{2322}{395}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{2322}{395} y=-\frac{362}{395} z=\frac{788}{395}$$