Whakaoti i te {l}{x^2+y^2=1}{x+y=3}

$$\left. \begin{array} { l } { x ^ { 2 } + y ^ { 2 } = 1 } \\ { x + y = 3 } \end{array} \right.$$

Whakaoti mō x, y (complex solution)

$$x=\frac{3+\sqrt{7}i}{2}\approx 1.5+1.322875656i\text{, }y=\frac{-\sqrt{7}i+3}{2}\approx 1.5-1.322875656i$$

$$x=\frac{-\sqrt{7}i+3}{2}\approx 1.5-1.322875656i\text{, }y=\frac{3+\sqrt{7}i}{2}\approx 1.5+1.322875656i$$

Ngā Upane e Whakamahi ana i te Whakakapinga me te Tikanga Tātai Pūrua

Whakaotia te x+y=3 mō x mā te wehe i te x i te taha mauī o te tohu ōrite.

$$x+y=3$$

Me tango y mai i ngā taha e rua o te whārite.

$$x=-y+3$$

Whakakapia te -y+3 mō te x ki tērā atu whārite, y^{2}+x^{2}=1.

$$y^{2}+\left(-y+3\right)^{2}=1$$

Pūrua -y+3.

$$y^{2}+y^{2}-6y+9=1$$

Tāpiri y^{2} ki te y^{2}.

$$2y^{2}-6y+9=1$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$2y^{2}-6y+8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1+1\left(-1\right)^{2} mō a, 1\times 3\left(-1\right)\times 2 mō b, me 8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 2\times 8}}{2\times 2}$$

Pūrua 1\times 3\left(-1\right)\times 2.

$$y=\frac{-\left(-6\right)±\sqrt{36-4\times 2\times 8}}{2\times 2}$$

Whakareatia -4 ki te 1+1\left(-1\right)^{2}.

$$y=\frac{-\left(-6\right)±\sqrt{36-8\times 8}}{2\times 2}$$

Whakareatia -8 ki te 8.

$$y=\frac{-\left(-6\right)±\sqrt{36-64}}{2\times 2}$$

Tāpiri 36 ki te -64.

$$y=\frac{-\left(-6\right)±\sqrt{-28}}{2\times 2}$$

Tuhia te pūtakerua o te -28.

$$y=\frac{-\left(-6\right)±2\sqrt{7}i}{2\times 2}$$

Ko te tauaro o 1\times 3\left(-1\right)\times 2 ko 6.

$$y=\frac{6±2\sqrt{7}i}{2\times 2}$$

Whakareatia 2 ki te 1+1\left(-1\right)^{2}.

$$y=\frac{6±2\sqrt{7}i}{4}$$

Nā, me whakaoti te whārite y=\frac{6±2\sqrt{7}i}{4} ina he tāpiri te ±. Tāpiri 6 ki te 2i\sqrt{7}.

$$y=\frac{6+2\sqrt{7}i}{4}$$

Whakawehe 6+2i\sqrt{7} ki te 4.

$$y=\frac{3+\sqrt{7}i}{2}$$

Nā, me whakaoti te whārite y=\frac{6±2\sqrt{7}i}{4} ina he tango te ±. Tango 2i\sqrt{7} mai i 6.

$$y=\frac{-2\sqrt{7}i+6}{4}$$

Whakawehe 6-2i\sqrt{7} ki te 4.

$$y=\frac{-\sqrt{7}i+3}{2}$$

E rua ngā otinga mō y: \frac{3+i\sqrt{7}}{2} me \frac{3-i\sqrt{7}}{2}. Me whakakapi \frac{3+i\sqrt{7}}{2} mō y ki te whārite x=-y+3 hei kimi i te otinga hāngai mō x e pai ai ki ngā whārite e rua.

$$x=-\frac{3+\sqrt{7}i}{2}+3$$

Me whakakapi te \frac{3-i\sqrt{7}}{2} ināianei mō te y ki te whārite x=-y+3 ka whakaoti hei kimi i te otinga hāngai mō x e pai ai ki ngā whārite e rua.

$$x=-\frac{-\sqrt{7}i+3}{2}+3$$

Kua oti te pūnaha te whakatau.

$$x=-\frac{3+\sqrt{7}i}{2}+3,y=\frac{3+\sqrt{7}i}{2}\text{ or }x=-\frac{-\sqrt{7}i+3}{2}+3,y=\frac{-\sqrt{7}i+3}{2}$$