Whakaoti i te {l}{2x+y+z=12}{2x-y+z=7}{x+2y-z=6}

$$\left. \begin{array} { l } { 2 x + y + z = 12 } \\ { 2 x - y + z = 7 } \\ { x + 2 y - z = 6 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

$$y = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

$$z = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te 2x+y+z=12 mō y.

$$y=-2x-z+12$$

Whakakapia te -2x-z+12 mō te y i te whārite tuarua me te tuatoru.

$$2x-\left(-2x-z+12\right)+z=7 x+2\left(-2x-z+12\right)-z=6$$

Me whakaoti ēnei whārite mō x me z takitahi.

$$x=-\frac{1}{2}z+\frac{19}{4} z=6-x$$

Whakakapia te -\frac{1}{2}z+\frac{19}{4} mō te x i te whārite z=6-x.

$$z=6-\left(-\frac{1}{2}z+\frac{19}{4}\right)$$

Me whakaoti te z=6-\left(-\frac{1}{2}z+\frac{19}{4}\right) mō z.

$$z=\frac{5}{2}$$

Whakakapia te \frac{5}{2} mō te z i te whārite x=-\frac{1}{2}z+\frac{19}{4}.

$$x=-\frac{1}{2}\times \frac{5}{2}+\frac{19}{4}$$

Tātaitia te x i te x=-\frac{1}{2}\times \frac{5}{2}+\frac{19}{4}.

$$x=\frac{7}{2}$$

Whakakapia te \frac{7}{2} mō te x me te \frac{5}{2} mō z i te whārite y=-2x-z+12.

$$y=-2\times \frac{7}{2}-\frac{5}{2}+12$$

Tātaitia te y i te y=-2\times \frac{7}{2}-\frac{5}{2}+12.

$$y=\frac{5}{2}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{7}{2} y=\frac{5}{2} z=\frac{5}{2}$$