Whakaoti i te {l}{4x+3y-2z=-11}{3x-7y+3z=10}{9x-8y+5z=9}

$$\left\{ \begin{array} { l } { 4 x + 3 y - 2 z = - 11 } \\ { 3 x - 7 y + 3 z = 10 } \\ { 9 x - 8 y + 5 z = 9 } \end{array} \right.$$

Whakaoti mō x, y, z

$$x=-1$$

$$y=-1$$

$$z=2$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te 4x+3y-2z=-11 mō x.

$$x=-\frac{3}{4}y+\frac{1}{2}z-\frac{11}{4}$$

Whakakapia te -\frac{3}{4}y+\frac{1}{2}z-\frac{11}{4} mō te x i te whārite tuarua me te tuatoru.

$$3\left(-\frac{3}{4}y+\frac{1}{2}z-\frac{11}{4}\right)-7y+3z=10 9\left(-\frac{3}{4}y+\frac{1}{2}z-\frac{11}{4}\right)-8y+5z=9$$

Me whakaoti ēnei whārite mō y me z takitahi.

$$y=-\frac{73}{37}+\frac{18}{37}z z=\frac{135}{38}+\frac{59}{38}y$$

Whakakapia te -\frac{73}{37}+\frac{18}{37}z mō te y i te whārite z=\frac{135}{38}+\frac{59}{38}y.

$$z=\frac{135}{38}+\frac{59}{38}\left(-\frac{73}{37}+\frac{18}{37}z\right)$$

Me whakaoti te z=\frac{135}{38}+\frac{59}{38}\left(-\frac{73}{37}+\frac{18}{37}z\right) mō z.

$$z=2$$

Whakakapia te 2 mō te z i te whārite y=-\frac{73}{37}+\frac{18}{37}z.

$$y=-\frac{73}{37}+\frac{18}{37}\times 2$$

Tātaitia te y i te y=-\frac{73}{37}+\frac{18}{37}\times 2.

$$y=-1$$

Whakakapia te -1 mō te y me te 2 mō z i te whārite x=-\frac{3}{4}y+\frac{1}{2}z-\frac{11}{4}.

$$x=-\frac{3}{4}\left(-1\right)+\frac{1}{2}\times 2-\frac{11}{4}$$

Tātaitia te x i te x=-\frac{3}{4}\left(-1\right)+\frac{1}{2}\times 2-\frac{11}{4}.

$$x=-1$$

Kua oti te pūnaha te whakatau.

$$x=-1 y=-1 z=2$$