Whakaoti i te {l}{x^2+y^2=18}{x-y=6}

$$\left. \begin{array} { l } { x ^ { 2 } + y ^ { 2 } = 18 } \\ { x - y = 6 } \end{array} \right.$$

Whakaoti mō x, y

$$x=3$$

$$y=-3$$

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.

$$x-y=6,y^{2}+x^{2}=18$$

Whakaotia te x-y=6 mō x mā te wehe i te x i te taha mauī o te tohu ōrite.

$$x-y=6$$

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

$$x=y+6$$

Whakakapia te y+6 mō te x ki tērā atu whārite, y^{2}+x^{2}=18.

$$y^{2}+\left(y+6\right)^{2}=18$$

Pūrua y+6.

$$y^{2}+y^{2}+12y+36=18$$

Tāpiri y^{2} ki te y^{2}.

$$2y^{2}+12y+36=18$$

Me tango 18 mai i ngā taha e rua o te whārite.

$$2y^{2}+12y+18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1+1\times 1^{2} mō a, 1\times 6\times 1\times 2 mō b, me 18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-12±\sqrt{12^{2}-4\times 2\times 18}}{2\times 2}$$

Pūrua 1\times 6\times 1\times 2.

$$y=\frac{-12±\sqrt{144-4\times 2\times 18}}{2\times 2}$$

Whakareatia -4 ki te 1+1\times 1^{2}.

$$y=\frac{-12±\sqrt{144-8\times 18}}{2\times 2}$$

Whakareatia -8 ki te 18.

$$y=\frac{-12±\sqrt{144-144}}{2\times 2}$$

Tāpiri 144 ki te -144.

$$y=\frac{-12±\sqrt{0}}{2\times 2}$$

Tuhia te pūtakerua o te 0.

$$y=-\frac{12}{2\times 2}$$

Whakareatia 2 ki te 1+1\times 1^{2}.

$$y=-\frac{12}{4}$$

Whakawehe -12 ki te 4.

$$y=-3$$

E rua ngā otinga mō y: -3 me -3. Me whakakapi -3 mō y ki te whārite x=y+6 hei kimi i te otinga hāngai mō x e pai ai ki ngā whārite e rua.

$$x=-3+6$$

Tāpiri -3 ki te 6.

$$x=3$$

Kua oti te pūnaha te whakatau.

$$x=3,y=-3\text{ or }x=3,y=-3$$