Whakaoti i te {l}{-3x+4y+3z=16}{5x+5y+2z=13}{-4x+3y+4z=12}

$$\left\{ \begin{array}{l}{ - 3 x + 4 y + 3 z = 16 }\\{ 5 x + 5 y + 2 z = 13 }\\{ - 4 x + 3 y + 4 z = 12 }\end{array} \right.$$

Whakaoti mō x, y, z

$$x=-1$$

$$y=4$$

$$z=-1$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te -3x+4y+3z=16 mō x.

$$x=\frac{4}{3}y+z-\frac{16}{3}$$

Whakakapia te \frac{4}{3}y+z-\frac{16}{3} mō te x i te whārite tuarua me te tuatoru.

$$5\left(\frac{4}{3}y+z-\frac{16}{3}\right)+5y+2z=13 -4\left(\frac{4}{3}y+z-\frac{16}{3}\right)+3y+4z=12$$

Me whakaoti ēnei whārite mō z me y takitahi.

$$z=\frac{17}{3}-\frac{5}{3}y y=4$$

Whakakapia te 4 mō te y i te whārite z=\frac{17}{3}-\frac{5}{3}y.

$$z=\frac{17}{3}-\frac{5}{3}\times 4$$

Tātaitia te z i te z=\frac{17}{3}-\frac{5}{3}\times 4.

$$z=-1$$

Whakakapia te -1 mō te z me te 4 mō y i te whārite x=\frac{4}{3}y+z-\frac{16}{3}.

$$x=\frac{4}{3}\times 4-1-\frac{16}{3}$$

Tātaitia te x i te x=\frac{4}{3}\times 4-1-\frac{16}{3}.

$$x=-1$$

Kua oti te pūnaha te whakatau.

$$x=-1 y=4 z=-1$$