Whakaoti i te x+y=3,x^2+y^2=5

$$x + y = 3 , x ^ { 2 } + y ^ { 2 } = 5$$

Whakaoti mō x, y

$$x=2\text{, }y=1$$

$$x=1\text{, }y=2$$

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

Hei whakaoti i ētahi whārite takirua mā te whakakapinga, me whakaoti tētahi whārite i te tuatahi mō tētahi o ngā taurangi. Ka whakakapi i te otinga mō taua taurangi ki tērā o ngā whārite.

$$x+y=3,y^{2}+x^{2}=5$$

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}=5.

$$y^{2}+\left(-y+3\right)^{2}=5$$

Pūrua -y+3.

$$y^{2}+y^{2}-6y+9=5$$

Tāpiri y^{2} ki te y^{2}.

$$2y^{2}-6y+9=5$$

Me tango 5 mai i ngā taha e rua o te whārite.

$$2y^{2}-6y+4=0$$

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 4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

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

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

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

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

Whakareatia -8 ki te 4.

$$y=\frac{-\left(-6\right)±\sqrt{36-32}}{2\times 2}$$

Tāpiri 36 ki te -32.

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

Tuhia te pūtakerua o te 4.

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

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

$$y=\frac{6±2}{2\times 2}$$

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

$$y=\frac{6±2}{4}$$

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

$$y=\frac{8}{4}$$

Whakawehe 8 ki te 4.

$$y=2$$

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

$$y=\frac{4}{4}$$

Whakawehe 4 ki te 4.

$$y=1$$

E rua ngā otinga mō y: 2 me 1. Me whakakapi 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.

$$x=-2+3$$

Tāpiri -2 ki te 3.

$$x=1$$

Me whakakapi te 1 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.

$$x=-1+3$$

Tāpiri -1 ki te 3.

$$x=2$$

Kua oti te pūnaha te whakatau.

$$x=1,y=2\text{ or }x=2,y=1$$