Whakaoti i te {l}{x+y=7}{x^2+y^2=25}

$$\left\{ \begin{array} { l } { x + y = 7 } \\ { x ^ { 2 } + y ^ { 2 } = 25 } \end{array} \right.$$

Whakaoti mō x, y

$$x=4\text{, }y=3$$

$$x=3\text{, }y=4$$

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.

$$x+y=7,y^{2}+x^{2}=25$$

Whakaotia te x+y=7 mō x mā te wehe i te x i te taha mauī o te tohu ōrite.

$$x+y=7$$

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

$$x=-y+7$$

Whakakapia te -y+7 mō te x ki tērā atu whārite, y^{2}+x^{2}=25.

$$y^{2}+\left(-y+7\right)^{2}=25$$

Pūrua -y+7.

$$y^{2}+y^{2}-14y+49=25$$

Tāpiri y^{2} ki te y^{2}.

$$2y^{2}-14y+49=25$$

Me tango 25 mai i ngā taha e rua o te whārite.

$$2y^{2}-14y+24=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1+1\left(-1\right)^{2} mō a, 1\times 7\left(-1\right)\times 2 mō b, me 24 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 2\times 24}}{2\times 2}$$

Pūrua 1\times 7\left(-1\right)\times 2.

$$y=\frac{-\left(-14\right)±\sqrt{196-4\times 2\times 24}}{2\times 2}$$

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

$$y=\frac{-\left(-14\right)±\sqrt{196-8\times 24}}{2\times 2}$$

Whakareatia -8 ki te 24.

$$y=\frac{-\left(-14\right)±\sqrt{196-192}}{2\times 2}$$

Tāpiri 196 ki te -192.

$$y=\frac{-\left(-14\right)±\sqrt{4}}{2\times 2}$$

Tuhia te pūtakerua o te 4.

$$y=\frac{-\left(-14\right)±2}{2\times 2}$$

Ko te tauaro o 1\times 7\left(-1\right)\times 2 ko 14.

$$y=\frac{14±2}{2\times 2}$$

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

$$y=\frac{14±2}{4}$$

Nā, me whakaoti te whārite y=\frac{14±2}{4} ina he tāpiri te ±. Tāpiri 14 ki te 2.

$$y=\frac{16}{4}$$

Whakawehe 16 ki te 4.

$$y=4$$

Nā, me whakaoti te whārite y=\frac{14±2}{4} ina he tango te ±. Tango 2 mai i 14.

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

Whakawehe 12 ki te 4.

$$y=3$$

E rua ngā otinga mō y: 4 me 3. Me whakakapi 4 mō y ki te whārite x=-y+7 hei kimi i te otinga hāngai mō x e pai ai ki ngā whārite e rua.

$$x=-4+7$$

Tāpiri -4 ki te 7.

$$x=3$$

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

$$x=-3+7$$

Tāpiri -3 ki te 7.

$$x=4$$

Kua oti te pūnaha te whakatau.

$$x=3,y=4\text{ or }x=4,y=3$$