Whakaoti i te {l}{3x+2y+5z=2}{5x-3y-2z=4}{2x-5y-3z=14}

$$\left. \begin{array} { l } { 3 x + 2 y + 5 z = 2 } \\ { 5 x - 3 y - 2 z = 4 } \\ { 2 x - 5 y - 3 z = 14 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=-1$$

$$y=-5$$

$$z=3$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te 3x+2y+5z=2 mō x.

$$x=-\frac{2}{3}y-\frac{5}{3}z+\frac{2}{3}$$

Whakakapia te -\frac{2}{3}y-\frac{5}{3}z+\frac{2}{3} mō te x i te whārite tuarua me te tuatoru.

$$5\left(-\frac{2}{3}y-\frac{5}{3}z+\frac{2}{3}\right)-3y-2z=4 2\left(-\frac{2}{3}y-\frac{5}{3}z+\frac{2}{3}\right)-5y-3z=14$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=-\frac{2}{19}-\frac{31}{19}z z=-2-y$$

Whakakapia te -\frac{2}{19}-\frac{31}{19}z mō te y i te whārite z=-2-y.

$$z=-2-\left(-\frac{2}{19}-\frac{31}{19}z\right)$$

Me whakaoti te z=-2-\left(-\frac{2}{19}-\frac{31}{19}z\right) mō z.

$$z=3$$

Whakakapia te 3 mō te z i te whārite y=-\frac{2}{19}-\frac{31}{19}z.

$$y=-\frac{2}{19}-\frac{31}{19}\times 3$$

Tātaitia te y i te y=-\frac{2}{19}-\frac{31}{19}\times 3.

$$y=-5$$

Whakakapia te -5 mō te y me te 3 mō z i te whārite x=-\frac{2}{3}y-\frac{5}{3}z+\frac{2}{3}.

$$x=-\frac{2}{3}\left(-5\right)-\frac{5}{3}\times 3+\frac{2}{3}$$

Tātaitia te x i te x=-\frac{2}{3}\left(-5\right)-\frac{5}{3}\times 3+\frac{2}{3}.

$$x=-1$$

Kua oti te pūnaha te whakatau.

$$x=-1 y=-5 z=3$$