Réitigh {l}{x^2/4+y^2=1}{y=frac{sqrt{2}}{4}x}

$$\left. \begin{array} { l } { \frac { x ^ { 2 } } { 4 } + y ^ { 2 } = 1 } \\ { y = \frac { \sqrt { 2 } } { 4 } x } \end{array} \right.$$

Réitigh do x,y.

$$x=-\frac{2\sqrt{6}}{3}\approx -1.632993162\text{, }y=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

$$x=\frac{2\sqrt{6}}{3}\approx 1.632993162\text{, }y=\frac{\sqrt{3}}{3}\approx 0.577350269$$

Céimeanna ag Baint Úsáid as Ionadú agus an bhFoirme Chearnach

Cuir an chéad cothromóid san áireamh. Méadaigh an dá thaobh den chothromóid faoi 4.

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

Cuir an dara cothromóid san áireamh. Scríobh \frac{\sqrt{2}}{4}x mar chodán aonair.

$$y=\frac{\sqrt{2}x}{4}$$

Bain \frac{\sqrt{2}x}{4} ón dá thaobh.

$$y-\frac{\sqrt{2}x}{4}=0$$

Méadaigh an dá thaobh den chothromóid faoi 4.

$$4y-\sqrt{2}x=0$$

Athordaigh na téarmaí.

$$-\sqrt{2}x+4y=0$$

Chun péire cothromóidí a réiteach ag baint úsáid as ionadú, réitigh ceann de na cothromóidí ar dtús le ceann de na hathróga a fháil. Ansin ionadaigh an toradh don athróg sin sa chothromóid eile.

$$\left(-\sqrt{2}\right)x+4y=0,4y^{2}+x^{2}=4$$

Réitigh \left(-\sqrt{2}\right)x+4y=0 do x trí x ar an taobh clé den chomhartha ‘Cothrom le’ a aonrú.

$$\left(-\sqrt{2}\right)x+4y=0$$

Bain 4y ón dá thaobh den chothromóid.

$$\left(-\sqrt{2}\right)x=-4y$$

Roinn an dá thaobh faoi -\sqrt{2}.

$$x=2\sqrt{2}y$$

Cuir x in aonad 2\sqrt{2}y sa chothromóid eile, 4y^{2}+x^{2}=4.

$$4y^{2}+\left(2\sqrt{2}y\right)^{2}=4$$

Cearnóg 2\sqrt{2}y.

$$4y^{2}+\left(2\sqrt{2}\right)^{2}y^{2}=4$$

Suimigh 4y^{2} le \left(2\sqrt{2}\right)^{2}y^{2}?

$$\left(\left(2\sqrt{2}\right)^{2}+4\right)y^{2}=4$$

Bain 4 ón dá thaobh den chothromóid.

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

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir 4+1\times \left(2\sqrt{2}\right)^{2} in ionad a, 1\times 0\times 2\times 2\sqrt{2} in ionad b, agus -4 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Cearnóg 1\times 0\times 2\times 2\sqrt{2}.

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

Méadaigh -4 faoi 4+1\times \left(2\sqrt{2}\right)^{2}.

$$y=\frac{0±\sqrt{-48\left(-4\right)}}{2\left(\left(2\sqrt{2}\right)^{2}+4\right)}$$

Méadaigh -48 faoi -4.

$$y=\frac{0±\sqrt{192}}{2\left(\left(2\sqrt{2}\right)^{2}+4\right)}$$

Tóg fréamh chearnach 192.

$$y=\frac{0±8\sqrt{3}}{2\left(\left(2\sqrt{2}\right)^{2}+4\right)}$$

Méadaigh 2 faoi 4+1\times \left(2\sqrt{2}\right)^{2}.

$$y=\frac{0±8\sqrt{3}}{24}$$

Réitigh an chothromóid y=\frac{0±8\sqrt{3}}{24} nuair is ionann ± agus plus.

$$y=\frac{\sqrt{3}}{3}$$

Réitigh an chothromóid y=\frac{0±8\sqrt{3}}{24} nuair is ionann ± agus míneas.

$$y=-\frac{\sqrt{3}}{3}$$

Tá dhá réiteach ann do y: \frac{\sqrt{3}}{3} agus -\frac{\sqrt{3}}{3}. Cuir y in aonad \frac{\sqrt{3}}{3} sa chothromóid eile x=2\sqrt{2}y chun an réiteach comhfhreagrach do x a shásaíonn an dá chothromóid a fháil.

$$x=2\sqrt{2}\times \frac{\sqrt{3}}{3}$$

Ansin cuir y in aonad -\frac{\sqrt{3}}{3} sa chothromóid eile x=2\sqrt{2}y agus faigh réiteach chun an réiteach comhfhreagrach do x a shásaíonn an dá chothromóid a fháil.

$$x=2\sqrt{2}\left(-\frac{\sqrt{3}}{3}\right)$$

Tá an córas réitithe anois.

$$x=2\sqrt{2}\times \frac{\sqrt{3}}{3},y=\frac{\sqrt{3}}{3}\text{ or }x=2\sqrt{2}\left(-\frac{\sqrt{3}}{3}\right),y=-\frac{\sqrt{3}}{3}$$