Réitigh {l}{x+y-1=0}{x^2+y^2-36=0}

$$\left. \begin{array} { l } { x + y - 1 = 0 } \\ { x ^ { 2 } + y ^ { 2 } - 36 = 0 } \end{array} \right.$$

Réitigh do x,y.

$$x=\frac{\sqrt{71}+1}{2}\approx 4.713074887\text{, }y=\frac{1-\sqrt{71}}{2}\approx -3.713074887$$

$$x=\frac{1-\sqrt{71}}{2}\approx -3.713074887\text{, }y=\frac{\sqrt{71}+1}{2}\approx 4.713074887$$

Céimeanna ag Baint Úsáid as Ionadú agus an bhFoirme Chearnach

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.

$$x+y-1=0,y^{2}+x^{2}-36=0$$

Réitigh x+y-1=0 do x trí x ar an taobh clé den chomhartha ‘Cothrom le’ a aonrú.

$$x+y-1=0$$

Cuir 1 leis an dá thaobh den chothromóid.

$$x+y=1$$

Bain y ón dá thaobh den chothromóid.

$$x=-y+1$$

Cuir x in aonad -y+1 sa chothromóid eile, y^{2}+x^{2}-36=0.

$$y^{2}+\left(-y+1\right)^{2}-36=0$$

Cearnóg -y+1.

$$y^{2}+y^{2}-2y+1-36=0$$

Suimigh y^{2} le y^{2}?

$$2y^{2}-2y+1-36=0$$

Suimigh 1\times 1^{2} le -36?

$$2y^{2}-2y-35=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir 1+1\left(-1\right)^{2} in ionad a, 1\times 1\left(-1\right)\times 2 in ionad b, agus -35 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 2\left(-35\right)}}{2\times 2}$$

Cearnóg 1\times 1\left(-1\right)\times 2.

$$y=\frac{-\left(-2\right)±\sqrt{4-4\times 2\left(-35\right)}}{2\times 2}$$

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

$$y=\frac{-\left(-2\right)±\sqrt{4-8\left(-35\right)}}{2\times 2}$$

Méadaigh -8 faoi -35.

$$y=\frac{-\left(-2\right)±\sqrt{4+280}}{2\times 2}$$

Suimigh 4 le 280?

$$y=\frac{-\left(-2\right)±\sqrt{284}}{2\times 2}$$

Tóg fréamh chearnach 284.

$$y=\frac{-\left(-2\right)±2\sqrt{71}}{2\times 2}$$

Tá 2 urchomhairleach le 1\times 1\left(-1\right)\times 2.

$$y=\frac{2±2\sqrt{71}}{2\times 2}$$

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

$$y=\frac{2±2\sqrt{71}}{4}$$

Réitigh an chothromóid y=\frac{2±2\sqrt{71}}{4} nuair is ionann ± agus plus. Suimigh 2 le 2\sqrt{71}?

$$y=\frac{2\sqrt{71}+2}{4}$$

Roinn 2+2\sqrt{71} faoi 4.

$$y=\frac{\sqrt{71}+1}{2}$$

Réitigh an chothromóid y=\frac{2±2\sqrt{71}}{4} nuair is ionann ± agus míneas. Dealaigh 2\sqrt{71} ó 2.

$$y=\frac{2-2\sqrt{71}}{4}$$

Roinn 2-2\sqrt{71} faoi 4.

$$y=\frac{1-\sqrt{71}}{2}$$

Tá dhá réiteach ann do y: \frac{1+\sqrt{71}}{2} agus \frac{1-\sqrt{71}}{2}. Cuir y in aonad \frac{1+\sqrt{71}}{2} sa chothromóid eile x=-y+1 chun an réiteach comhfhreagrach do x a shásaíonn an dá chothromóid a fháil.

$$x=-\frac{\sqrt{71}+1}{2}+1$$

Ansin cuir y in aonad \frac{1-\sqrt{71}}{2} sa chothromóid eile x=-y+1 agus faigh réiteach chun an réiteach comhfhreagrach do x a shásaíonn an dá chothromóid a fháil.

$$x=-\frac{1-\sqrt{71}}{2}+1$$

Tá an córas réitithe anois.

$$x=-\frac{\sqrt{71}+1}{2}+1,y=\frac{\sqrt{71}+1}{2}\text{ or }x=-\frac{1-\sqrt{71}}{2}+1,y=\frac{1-\sqrt{71}}{2}$$