Whakaoti i te {l}{5y=10x}{x^2+y^2=36}

$$\left\{ \begin{array} { l } { 5 y = 10 x } \\ { x ^ { 2 } + y ^ { 2 } = 36 } \end{array} \right.$$

Whakaoti mō y, x

$$x=-\frac{6\sqrt{5}}{5}\approx -2.683281573\text{, }y=-\frac{12\sqrt{5}}{5}\approx -5.366563146$$

$$x=\frac{6\sqrt{5}}{5}\approx 2.683281573\text{, }y=\frac{12\sqrt{5}}{5}\approx 5.366563146$$

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

Whakaarohia te whārite tuatahi. Tangohia te 10x mai i ngā taha e rua.

$$5y-10x=0$$

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.

$$5y-10x=0,x^{2}+y^{2}=36$$

Whakaotia te 5y-10x=0 mō y mā te wehe i te y i te taha mauī o te tohu ōrite.

$$5y-10x=0$$

Me tango -10x mai i ngā taha e rua o te whārite.

$$5y=10x$$

Whakawehea ngā taha e rua ki te 5.

$$y=2x$$

Whakakapia te 2x mō te y ki tērā atu whārite, x^{2}+y^{2}=36.

$$x^{2}+\left(2x\right)^{2}=36$$

Pūrua 2x.

$$x^{2}+4x^{2}=36$$

Tāpiri x^{2} ki te 4x^{2}.

$$5x^{2}=36$$

Me tango 36 mai i ngā taha e rua o te whārite.

$$5x^{2}-36=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1+1\times 2^{2} mō a, 1\times 0\times 2\times 2 mō b, me -36 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-36\right)}}{2\times 5}$$

Pūrua 1\times 0\times 2\times 2.

$$x=\frac{0±\sqrt{-4\times 5\left(-36\right)}}{2\times 5}$$

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

$$x=\frac{0±\sqrt{-20\left(-36\right)}}{2\times 5}$$

Whakareatia -20 ki te -36.

$$x=\frac{0±\sqrt{720}}{2\times 5}$$

Tuhia te pūtakerua o te 720.

$$x=\frac{0±12\sqrt{5}}{2\times 5}$$

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

$$x=\frac{0±12\sqrt{5}}{10}$$

Nā, me whakaoti te whārite x=\frac{0±12\sqrt{5}}{10} ina he tāpiri te ±.

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

Nā, me whakaoti te whārite x=\frac{0±12\sqrt{5}}{10} ina he tango te ±.

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

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

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

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

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

Kua oti te pūnaha te whakatau.

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