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

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

Whakaoti mō x, y, z

$$x = \frac{11}{7} = 1\frac{4}{7} \approx 1.571428571$$

$$y = \frac{33}{7} = 4\frac{5}{7} \approx 4.714285714$$

$$z = -\frac{22}{7} = -3\frac{1}{7} \approx -3.142857143$$

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.

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

Me whakaoti ēnei whārite mō y me x takitahi.

$$y=-4x+11 x=-\frac{3}{5}y+\frac{22}{5}$$

Whakakapia te -4x+11 mō te y i te whārite x=-\frac{3}{5}y+\frac{22}{5}.

$$x=-\frac{3}{5}\left(-4x+11\right)+\frac{22}{5}$$

Me whakaoti te x=-\frac{3}{5}\left(-4x+11\right)+\frac{22}{5} mō x.

$$x=\frac{11}{7}$$

Whakakapia te \frac{11}{7} mō te x i te whārite y=-4x+11.

$$y=-4\times \frac{11}{7}+11$$

Tātaitia te y i te y=-4\times \frac{11}{7}+11.

$$y=\frac{33}{7}$$

Whakakapia te \frac{33}{7} mō te y me te \frac{11}{7} mō x i te whārite z=-3x-2y+11.

$$z=-3\times \frac{11}{7}-2\times \frac{33}{7}+11$$

Tātaitia te z i te z=-3\times \frac{11}{7}-2\times \frac{33}{7}+11.

$$z=-\frac{22}{7}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{11}{7} y=\frac{33}{7} z=-\frac{22}{7}$$