Whakaoti i te {l}{a+b+c=3}{a-2b+4c=5}{3b+4c=5}

$$\left\{ \begin{array} { l } { a + b + c = 3 } \\ { a - 2 b + 4 c = 5 } \\ { 3 b + 4 c = 5 } \end{array} \right.$$

Whakaoti mō a, b, c

$$a = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

$$b=\frac{1}{3}\approx 0.333333333$$

$$c=1$$

Ngā Hipanga Poto E Whakamahi Whakakapinga Ana

Me whakaoti te a+b+c=3 mō a.

$$a=-b-c+3$$

Whakakapia te -b-c+3 mō te a i te whārite a-2b+4c=5.

$$-b-c+3-2b+4c=5$$

Me whakaoti te whārite tuarua mō b me te whārite tuatoru mō c.

$$b=c-\frac{2}{3} c=-\frac{3}{4}b+\frac{5}{4}$$

Whakakapia te c-\frac{2}{3} mō te b i te whārite c=-\frac{3}{4}b+\frac{5}{4}.

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

Me whakaoti te c=-\frac{3}{4}\left(c-\frac{2}{3}\right)+\frac{5}{4} mō c.

$$c=1$$

Whakakapia te 1 mō te c i te whārite b=c-\frac{2}{3}.

$$b=1-\frac{2}{3}$$

Tātaitia te b i te b=1-\frac{2}{3}.

$$b=\frac{1}{3}$$

Whakakapia te \frac{1}{3} mō te b me te 1 mō c i te whārite a=-b-c+3.

$$a=-\frac{1}{3}-1+3$$

Tātaitia te a i te a=-\frac{1}{3}-1+3.

$$a=\frac{5}{3}$$

Kua oti te pūnaha te whakatau.

$$a=\frac{5}{3} b=\frac{1}{3} c=1$$