Whakaoti i te {c}{x^2+y^2=8}{x+y=4}

$$\left. \begin{array} { c } { x ^ { 2 } + y ^ { 2 } = 8 } \\ { x + y = 4 } \end{array} \right.$$

Whakaoti mō x, y

$$x=2$$

$$y=2$$

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.

$$x+y=4,y^{2}+x^{2}=8$$

Whakaotia te x+y=4 mō x mā te wehe i te x i te taha mauī o te tohu ōrite.

$$x+y=4$$

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

$$x=-y+4$$

Whakakapia te -y+4 mō te x ki tērā atu whārite, y^{2}+x^{2}=8.

$$y^{2}+\left(-y+4\right)^{2}=8$$

Pūrua -y+4.

$$y^{2}+y^{2}-8y+16=8$$

Tāpiri y^{2} ki te y^{2}.

$$2y^{2}-8y+16=8$$

Me tango 8 mai i ngā taha e rua o te whārite.

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

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

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

Pūrua 1\times 4\left(-1\right)\times 2.

$$y=\frac{-\left(-8\right)±\sqrt{64-4\times 2\times 8}}{2\times 2}$$

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

$$y=\frac{-\left(-8\right)±\sqrt{64-8\times 8}}{2\times 2}$$

Whakareatia -8 ki te 8.

$$y=\frac{-\left(-8\right)±\sqrt{64-64}}{2\times 2}$$

Tāpiri 64 ki te -64.

$$y=\frac{-\left(-8\right)±\sqrt{0}}{2\times 2}$$

Tuhia te pūtakerua o te 0.

$$y=-\frac{-8}{2\times 2}$$

Ko te tauaro o 1\times 4\left(-1\right)\times 2 ko 8.

$$y=\frac{8}{2\times 2}$$

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

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

Whakawehe 8 ki te 4.

$$y=2$$

E rua ngā otinga mō y: 2 me 2. Me whakakapi 2 mō y ki te whārite x=-y+4 hei kimi i te otinga hāngai mō x e pai ai ki ngā whārite e rua.

$$x=-2+4$$

Tāpiri -2 ki te 4.

$$x=2$$

Kua oti te pūnaha te whakatau.

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