Whakaoti i te {l}{3x+y+2z=25}{x+3y+z=12}{x+y+z=7}

$$\left\{ \begin{array} { l } { 3 x + y + 2 z = 25 } \\ { x + 3 y + z = 12 } \\ { x + y + z = 7 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x = \frac{27}{2} = 13\frac{1}{2} = 13.5$$

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

$$z=-9$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te 3x+y+2z=25 mō y.

$$y=-3x-2z+25$$

Whakakapia te -3x-2z+25 mō te y i te whārite tuarua me te tuatoru.

$$x+3\left(-3x-2z+25\right)+z=12 x-3x-2z+25+z=7$$

Me whakaoti ēnei whārite mō x me z takitahi.

$$x=-\frac{5}{8}z+\frac{63}{8} z=-2x+18$$

Whakakapia te -\frac{5}{8}z+\frac{63}{8} mō te x i te whārite z=-2x+18.

$$z=-2\left(-\frac{5}{8}z+\frac{63}{8}\right)+18$$

Me whakaoti te z=-2\left(-\frac{5}{8}z+\frac{63}{8}\right)+18 mō z.

$$z=-9$$

Whakakapia te -9 mō te z i te whārite x=-\frac{5}{8}z+\frac{63}{8}.

$$x=-\frac{5}{8}\left(-9\right)+\frac{63}{8}$$

Tātaitia te x i te x=-\frac{5}{8}\left(-9\right)+\frac{63}{8}.

$$x=\frac{27}{2}$$

Whakakapia te \frac{27}{2} mō te x me te -9 mō z i te whārite y=-3x-2z+25.

$$y=-3\times \frac{27}{2}-2\left(-9\right)+25$$

Tātaitia te y i te y=-3\times \frac{27}{2}-2\left(-9\right)+25.

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

Kua oti te pūnaha te whakatau.

$$x=\frac{27}{2} y=\frac{5}{2} z=-9$$