Whakaoti i te {l}{3x^2-2y^2=25}{x+y=0}

$$\left. \begin{array}{l}{ 3 x ^ { 2 } - 2 y ^ { 2 } = 25 }\\{ x + y = 0 }\end{array} \right.$$

Whakaoti mō x, y

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

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

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.

$$x+y=0,-2y^{2}+3x^{2}=25$$

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

$$x+y=0$$

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

$$x=-y$$

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

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

Pūrua -y.

$$-2y^{2}+3y^{2}=25$$

Tāpiri -2y^{2} ki te 3y^{2}.

$$y^{2}=25$$

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

$$y^{2}-25=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2+3\left(-1\right)^{2} mō a, 3\times 0\left(-1\right)\times 2 mō b, me -25 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-25\right)}}{2}$$

Pūrua 3\times 0\left(-1\right)\times 2.

$$y=\frac{0±\sqrt{-4\left(-25\right)}}{2}$$

Whakareatia -4 ki te -25.

$$y=\frac{0±\sqrt{100}}{2}$$

Tuhia te pūtakerua o te 100.

$$y=\frac{0±10}{2}$$

Nā, me whakaoti te whārite y=\frac{0±10}{2} ina he tāpiri te ±. Whakawehe 10 ki te 2.

$$y=5$$

Nā, me whakaoti te whārite y=\frac{0±10}{2} ina he tango te ±. Whakawehe -10 ki te 2.

$$y=-5$$

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

$$x=-5$$

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

$$x=-\left(-5\right)$$

Whakareatia -1 ki te -5.

$$x=5$$

Kua oti te pūnaha te whakatau.

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