Whakaoti i te {l}{3x+2y+z=11}{5x+3y+4z=2}{x+y-z=1}

$$\left\{ \begin{array} { l } { 3 x + 2 y + z = 11 } \\ { 5 x + 3 y + 4 z = 2 } \\ { x + y - z = 1 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=66$$

$$y=-84$$

$$z=-19$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te 3x+2y+z=11 mō z.

$$z=-3x-2y+11$$

Whakakapia te -3x-2y+11 mō te z i te whārite tuarua me te tuatoru.

$$5x+3y+4\left(-3x-2y+11\right)=2 x+y-\left(-3x-2y+11\right)=1$$

Me whakaoti ēnei whārite mō y me x takitahi.

$$y=\frac{42}{5}-\frac{7}{5}x x=3-\frac{3}{4}y$$

Whakakapia te \frac{42}{5}-\frac{7}{5}x mō te y i te whārite x=3-\frac{3}{4}y.

$$x=3-\frac{3}{4}\left(\frac{42}{5}-\frac{7}{5}x\right)$$

Me whakaoti te x=3-\frac{3}{4}\left(\frac{42}{5}-\frac{7}{5}x\right) mō x.

$$x=66$$

Whakakapia te 66 mō te x i te whārite y=\frac{42}{5}-\frac{7}{5}x.

$$y=\frac{42}{5}-\frac{7}{5}\times 66$$

Tātaitia te y i te y=\frac{42}{5}-\frac{7}{5}\times 66.

$$y=-84$$

Whakakapia te -84 mō te y me te 66 mō x i te whārite z=-3x-2y+11.

$$z=-3\times 66-2\left(-84\right)+11$$

Tātaitia te z i te z=-3\times 66-2\left(-84\right)+11.

$$z=-19$$

Kua oti te pūnaha te whakatau.

$$x=66 y=-84 z=-19$$