Whakaoti i te {l}{y=3x}{x^2+y^2=4}

$$\left\{ \begin{array} { l } { y = 3 x } \\ { x ^ { 2 } + y ^ { 2 } = 4 } \end{array} \right.$$

Whakaoti mō y, x

$$x=-\frac{\sqrt{10}}{5}\approx -0.632455532\text{, }y=-\frac{3\sqrt{10}}{5}\approx -1.897366596$$

$$x=\frac{\sqrt{10}}{5}\approx 0.632455532\text{, }y=\frac{3\sqrt{10}}{5}\approx 1.897366596$$

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

Whakaarohia te whārite tuatahi. Tangohia te 3x mai i ngā taha e rua.

$$y-3x=0$$

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.

$$y-3x=0,x^{2}+y^{2}=4$$

Whakaotia te y-3x=0 mō y mā te wehe i te y i te taha mauī o te tohu ōrite.

$$y-3x=0$$

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

$$y=3x$$

Whakakapia te 3x mō te y ki tērā atu whārite, x^{2}+y^{2}=4.

$$x^{2}+\left(3x\right)^{2}=4$$

Pūrua 3x.

$$x^{2}+9x^{2}=4$$

Tāpiri x^{2} ki te 9x^{2}.

$$10x^{2}=4$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$10x^{2}-4=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\times 10\left(-4\right)}}{2\times 10}$$

Pūrua 1\times 0\times 2\times 3.

$$x=\frac{0±\sqrt{-4\times 10\left(-4\right)}}{2\times 10}$$

Whakareatia -4 ki te 1+1\times 3^{2}.

$$x=\frac{0±\sqrt{-40\left(-4\right)}}{2\times 10}$$

Whakareatia -40 ki te -4.

$$x=\frac{0±\sqrt{160}}{2\times 10}$$

Tuhia te pūtakerua o te 160.

$$x=\frac{0±4\sqrt{10}}{2\times 10}$$

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

$$x=\frac{0±4\sqrt{10}}{20}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{10}}{20} ina he tāpiri te ±.

$$x=\frac{\sqrt{10}}{5}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{10}}{20} ina he tango te ±.

$$x=-\frac{\sqrt{10}}{5}$$

E rua ngā otinga mō x: \frac{\sqrt{10}}{5} me -\frac{\sqrt{10}}{5}. Me whakakapi \frac{\sqrt{10}}{5} mō x ki te whārite y=3x hei kimi i te otinga hāngai mō y e pai ai ki ngā whārite e rua.

$$y=3\times \frac{\sqrt{10}}{5}$$

Me whakakapi te -\frac{\sqrt{10}}{5} ināianei mō te x ki te whārite y=3x ka whakaoti hei kimi i te otinga hāngai mō y e pai ai ki ngā whārite e rua.

$$y=3\left(-\frac{\sqrt{10}}{5}\right)$$

Kua oti te pūnaha te whakatau.

$$y=3\times \frac{\sqrt{10}}{5},x=\frac{\sqrt{10}}{5}\text{ or }y=3\left(-\frac{\sqrt{10}}{5}\right),x=-\frac{\sqrt{10}}{5}$$