Whakaoti i te {l}{x^2+y^2=25}{x=3y-5}

$$\left. \begin{array} { l } { x ^ { 2 } + y ^ { 2 } = 25 } \\ { x = 3 y - 5 } \end{array} \right.$$

Whakaoti mō x, y

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

$$x=-5\text{, }y=0$$

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

Whakaarohia te whārite tuarua. Tangohia te 3y mai i ngā taha e rua.

$$x-3y=-5$$

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.

$$x-3y=-5,y^{2}+x^{2}=25$$

Whakaotia te x-3y=-5 mō x mā te wehe i te x i te taha mauī o te tohu ōrite.

$$x-3y=-5$$

Me tango -3y mai i ngā taha e rua o te whārite.

$$x=3y-5$$

Whakakapia te 3y-5 mō te x ki tērā atu whārite, y^{2}+x^{2}=25.

$$y^{2}+\left(3y-5\right)^{2}=25$$

Pūrua 3y-5.

$$y^{2}+9y^{2}-30y+25=25$$

Tāpiri y^{2} ki te 9y^{2}.

$$10y^{2}-30y+25=25$$

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

$$10y^{2}-30y=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1+1\times 3^{2} mō a, 1\left(-5\right)\times 2\times 3 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-30\right)±\sqrt{\left(-30\right)^{2}}}{2\times 10}$$

Tuhia te pūtakerua o te \left(-30\right)^{2}.

$$y=\frac{-\left(-30\right)±30}{2\times 10}$$

Ko te tauaro o 1\left(-5\right)\times 2\times 3 ko 30.

$$y=\frac{30±30}{2\times 10}$$

Whakareatia 2 ki te 1+1\times 3^{2}.

$$y=\frac{30±30}{20}$$

Nā, me whakaoti te whārite y=\frac{30±30}{20} ina he tāpiri te ±. Tāpiri 30 ki te 30.

$$y=\frac{60}{20}$$

Whakawehe 60 ki te 20.

$$y=3$$

Nā, me whakaoti te whārite y=\frac{30±30}{20} ina he tango te ±. Tango 30 mai i 30.

$$y=\frac{0}{20}$$

Whakawehe 0 ki te 20.

$$y=0$$

E rua ngā otinga mō y: 3 me 0. Me whakakapi 3 mō y ki te whārite x=3y-5 hei kimi i te otinga hāngai mō x e pai ai ki ngā whārite e rua.

$$x=3\times 3-5$$

Whakareatia 3 ki te 3.

$$x=9-5$$

Tāpiri 3\times 3 ki te -5.

$$x=4$$

Me whakakapi te 0 ināianei mō te y ki te whārite x=3y-5 ka whakaoti hei kimi i te otinga hāngai mō x e pai ai ki ngā whārite e rua.

$$x=-5$$

Kua oti te pūnaha te whakatau.

$$x=4,y=3\text{ or }x=-5,y=0$$