Whakaoti i te {l}{3/2y-x-1/2z=2.5}{2x-y-1/2z=-2}{2z-1/2x-frac{1}{2}y=2}

$$\left. \begin{array} { l } { \frac { 3 } { 2 } y - x - \frac { 1 } { 2 } z = 2.5 } \\ { 2 x - y - \frac { 1 } { 2 } z = - 2 } \\ { 2 z - \frac { 1 } { 2 } x - \frac { 1 } { 2 } y = 2 } \end{array} \right.$$

Whakaoti mō y, x, z

$$x=1$$

$$y=3$$

$$z=2$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te \frac{3}{2}y-x-\frac{1}{2}z=2.5 mō x.

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

Whakakapia te \frac{3}{2}y-\frac{1}{2}z-\frac{5}{2} mō te x i te whārite tuarua me te tuatoru.

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

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=\frac{3}{2}+\frac{3}{4}z z=\frac{1}{3}+\frac{5}{9}y$$

Whakakapia te \frac{3}{2}+\frac{3}{4}z mō te y i te whārite z=\frac{1}{3}+\frac{5}{9}y.

$$z=\frac{1}{3}+\frac{5}{9}\left(\frac{3}{2}+\frac{3}{4}z\right)$$

Me whakaoti te z=\frac{1}{3}+\frac{5}{9}\left(\frac{3}{2}+\frac{3}{4}z\right) mō z.

$$z=2$$

Whakakapia te 2 mō te z i te whārite y=\frac{3}{2}+\frac{3}{4}z.

$$y=\frac{3}{2}+\frac{3}{4}\times 2$$

Tātaitia te y i te y=\frac{3}{2}+\frac{3}{4}\times 2.

$$y=3$$

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

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

Tātaitia te x i te x=\frac{3}{2}\times 3-\frac{1}{2}\times 2-\frac{5}{2}.

$$x=1$$

Kua oti te pūnaha te whakatau.

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