Whakaoti i te {l}{2x+-y=0}{x^2+y^2=9}

$$\left\{ \begin{array} { l } { 2 x + - y = 0 } \\ { x ^ { 2 } + y ^ { 2 } = 9 } \end{array} \right.$$

Whakaoti mō x, y

$$x=-\frac{3\sqrt{5}}{5}\approx -1.341640786\text{, }y=-\frac{6\sqrt{5}}{5}\approx -2.683281573$$

$$x=\frac{3\sqrt{5}}{5}\approx 1.341640786\text{, }y=\frac{6\sqrt{5}}{5}\approx 2.683281573$$

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.

$$2x-y=0,y^{2}+x^{2}=9$$

Whakaotia te 2x-y=0 mō x mā te wehe i te x i te taha mauī o te tohu ōrite.

$$2x-y=0$$

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

$$2x=y$$

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{1}{2}y$$

Whakakapia te \frac{1}{2}y mō te x ki tērā atu whārite, y^{2}+x^{2}=9.

$$y^{2}+\left(\frac{1}{2}y\right)^{2}=9$$

Pūrua \frac{1}{2}y.

$$y^{2}+\frac{1}{4}y^{2}=9$$

Tāpiri y^{2} ki te \frac{1}{4}y^{2}.

$$\frac{5}{4}y^{2}=9$$

Me tango 9 mai i ngā taha e rua o te whārite.

$$\frac{5}{4}y^{2}-9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1+1\times \left(\frac{1}{2}\right)^{2} mō a, 1\times 0\times \frac{1}{2}\times 2 mō b, me -9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times \frac{5}{4}\left(-9\right)}}{2\times \frac{5}{4}}$$

Pūrua 1\times 0\times \frac{1}{2}\times 2.

$$y=\frac{0±\sqrt{-4\times \frac{5}{4}\left(-9\right)}}{2\times \frac{5}{4}}$$

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

$$y=\frac{0±\sqrt{-5\left(-9\right)}}{2\times \frac{5}{4}}$$

Whakareatia -5 ki te -9.

$$y=\frac{0±\sqrt{45}}{2\times \frac{5}{4}}$$

Tuhia te pūtakerua o te 45.

$$y=\frac{0±3\sqrt{5}}{2\times \frac{5}{4}}$$

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

$$y=\frac{0±3\sqrt{5}}{\frac{5}{2}}$$

Nā, me whakaoti te whārite y=\frac{0±3\sqrt{5}}{\frac{5}{2}} ina he tāpiri te ±.

$$y=\frac{6\sqrt{5}}{5}$$

Nā, me whakaoti te whārite y=\frac{0±3\sqrt{5}}{\frac{5}{2}} ina he tango te ±.

$$y=-\frac{6\sqrt{5}}{5}$$

E rua ngā otinga mō y: \frac{6\sqrt{5}}{5} me -\frac{6\sqrt{5}}{5}. Me whakakapi \frac{6\sqrt{5}}{5} mō y ki te whārite x=\frac{1}{2}y hei kimi i te otinga hāngai mō x e pai ai ki ngā whārite e rua.

$$x=\frac{1}{2}\times \frac{6\sqrt{5}}{5}$$

Whakareatia \frac{1}{2} ki te \frac{6\sqrt{5}}{5}.

$$x=\frac{6\sqrt{5}}{2\times 5}$$

Me whakakapi te -\frac{6\sqrt{5}}{5} ināianei mō te y ki te whārite x=\frac{1}{2}y ka whakaoti hei kimi i te otinga hāngai mō x e pai ai ki ngā whārite e rua.

$$x=\frac{1}{2}\left(-\frac{6\sqrt{5}}{5}\right)$$

Whakareatia \frac{1}{2} ki te -\frac{6\sqrt{5}}{5}.

$$x=-\frac{6\sqrt{5}}{2\times 5}$$

Kua oti te pūnaha te whakatau.

$$x=\frac{6\sqrt{5}}{2\times 5},y=\frac{6\sqrt{5}}{5}\text{ or }x=-\frac{6\sqrt{5}}{2\times 5},y=-\frac{6\sqrt{5}}{5}$$