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

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

Whakaoti mō x, y, z

$$x=-\frac{7}{19}\approx -0.368421053$$

$$y=-\frac{17}{19}\approx -0.894736842$$

$$z=\frac{12}{19}\approx 0.631578947$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me raupapa anō ngā whārite.

$$1+x=z 3x-4y+4z=5 -2x+5y-2z=-5$$

Me whakaoti te 1+x=z mō z.

$$z=1+x$$

Whakakapia te 1+x mō te z i te whārite tuarua me te tuatoru.

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

Me whakaoti ēnei whārite mō y me x takitahi.

$$y=\frac{7}{4}x-\frac{1}{4} x=\frac{5}{4}y+\frac{3}{4}$$

Whakakapia te \frac{7}{4}x-\frac{1}{4} mō te y i te whārite x=\frac{5}{4}y+\frac{3}{4}.

$$x=\frac{5}{4}\left(\frac{7}{4}x-\frac{1}{4}\right)+\frac{3}{4}$$

Me whakaoti te x=\frac{5}{4}\left(\frac{7}{4}x-\frac{1}{4}\right)+\frac{3}{4} mō x.

$$x=-\frac{7}{19}$$

Whakakapia te -\frac{7}{19} mō te x i te whārite y=\frac{7}{4}x-\frac{1}{4}.

$$y=\frac{7}{4}\left(-\frac{7}{19}\right)-\frac{1}{4}$$

Tātaitia te y i te y=\frac{7}{4}\left(-\frac{7}{19}\right)-\frac{1}{4}.

$$y=-\frac{17}{19}$$

Whakakapia te -\frac{7}{19} mō te x i te whārite z=1+x.

$$z=1-\frac{7}{19}$$

Tātaitia te z i te z=1-\frac{7}{19}.

$$z=\frac{12}{19}$$

Kua oti te pūnaha te whakatau.

$$x=-\frac{7}{19} y=-\frac{17}{19} z=\frac{12}{19}$$