Whakaoti i te {l}{y=x-5}{x^2+y^2=17}

$$\left. \begin{array} { l } { y = x - 5 } \\ { x ^ { 2 } + y ^ { 2 } = 17 } \end{array} \right.$$

Whakaoti mō y, x

$$x=4\text{, }y=-1$$

$$x=1\text{, }y=-4$$

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

Whakaarohia te whārite tuatahi. Tangohia te x mai i ngā taha e rua.

$$y-x=-5$$

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.

$$y-x=-5,x^{2}+y^{2}=17$$

Whakaotia te y-x=-5 mō y mā te wehe i te y i te taha mauī o te tohu ōrite.

$$y-x=-5$$

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

$$y=x-5$$

Whakakapia te x-5 mō te y ki tērā atu whārite, x^{2}+y^{2}=17.

$$x^{2}+\left(x-5\right)^{2}=17$$

Pūrua x-5.

$$x^{2}+x^{2}-10x+25=17$$

Tāpiri x^{2} ki te x^{2}.

$$2x^{2}-10x+25=17$$

Me tango 17 mai i ngā taha e rua o te whārite.

$$2x^{2}-10x+8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1+1\times 1^{2} mō a, 1\left(-5\right)\times 1\times 2 mō b, me 8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 2\times 8}}{2\times 2}$$

Pūrua 1\left(-5\right)\times 1\times 2.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\times 2\times 8}}{2\times 2}$$

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

$$x=\frac{-\left(-10\right)±\sqrt{100-8\times 8}}{2\times 2}$$

Whakareatia -8 ki te 8.

$$x=\frac{-\left(-10\right)±\sqrt{100-64}}{2\times 2}$$

Tāpiri 100 ki te -64.

$$x=\frac{-\left(-10\right)±\sqrt{36}}{2\times 2}$$

Tuhia te pūtakerua o te 36.

$$x=\frac{-\left(-10\right)±6}{2\times 2}$$

Ko te tauaro o 1\left(-5\right)\times 1\times 2 ko 10.

$$x=\frac{10±6}{2\times 2}$$

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

$$x=\frac{10±6}{4}$$

Nā, me whakaoti te whārite x=\frac{10±6}{4} ina he tāpiri te ±. Tāpiri 10 ki te 6.

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

Whakawehe 16 ki te 4.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{10±6}{4} ina he tango te ±. Tango 6 mai i 10.

$$x=\frac{4}{4}$$

Whakawehe 4 ki te 4.

$$x=1$$

E rua ngā otinga mō x: 4 me 1. Me whakakapi 4 mō x ki te whārite y=x-5 hei kimi i te otinga hāngai mō y e pai ai ki ngā whārite e rua.

$$y=4-5$$

Tāpiri 1\times 4 ki te -5.

$$y=-1$$

Me whakakapi te 1 ināianei mō te x ki te whārite y=x-5 ka whakaoti hei kimi i te otinga hāngai mō y e pai ai ki ngā whārite e rua.

$$y=1-5$$

Tāpiri 1\times 1 ki te -5.

$$y=-4$$

Kua oti te pūnaha te whakatau.

$$y=-1,x=4\text{ or }y=-4,x=1$$