Réitigh {l}{x^2+y^2=1}{x-5+y=0}

$$\left. \begin{array} { l } { x ^ { 2 } + y ^ { 2 } = 1 } \\ { x - 5 + y = 0 } \end{array} \right.$$

Réitigh do x,y. (complex solution)

$$x=\frac{5+\sqrt{23}i}{2}\approx 2.5+2.397915762i\text{, }y=\frac{-\sqrt{23}i+5}{2}\approx 2.5-2.397915762i$$

$$x=\frac{-\sqrt{23}i+5}{2}\approx 2.5-2.397915762i\text{, }y=\frac{5+\sqrt{23}i}{2}\approx 2.5+2.397915762i$$

Céimeanna ag Baint Úsáid as Ionadú agus an bhFoirme Chearnach

Réitigh x+y-5=0 do x trí x ar an taobh clé den chomhartha ‘Cothrom le’ a aonrú.

$$x+y-5=0$$

Cuir 5 leis an dá thaobh den chothromóid.

$$x+y=5$$

Bain y ón dá thaobh den chothromóid.

$$x=-y+5$$

Cuir x in aonad -y+5 sa chothromóid eile, y^{2}+x^{2}=1.

$$y^{2}+\left(-y+5\right)^{2}=1$$

Cearnóg -y+5.

$$y^{2}+y^{2}-10y+25=1$$

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

$$2y^{2}-10y+25=1$$

Bain 1 ón dá thaobh den chothromóid.

$$2y^{2}-10y+24=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir 1+1\left(-1\right)^{2} in ionad a, 1\times 5\left(-1\right)\times 2 in ionad b, agus 24 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 2\times 24}}{2\times 2}$$

Cearnóg 1\times 5\left(-1\right)\times 2.

$$y=\frac{-\left(-10\right)±\sqrt{100-4\times 2\times 24}}{2\times 2}$$

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

$$y=\frac{-\left(-10\right)±\sqrt{100-8\times 24}}{2\times 2}$$

Méadaigh -8 faoi 24.

$$y=\frac{-\left(-10\right)±\sqrt{100-192}}{2\times 2}$$

Suimigh 100 le -192?

$$y=\frac{-\left(-10\right)±\sqrt{-92}}{2\times 2}$$

Tóg fréamh chearnach -92.

$$y=\frac{-\left(-10\right)±2\sqrt{23}i}{2\times 2}$$

Tá 10 urchomhairleach le 1\times 5\left(-1\right)\times 2.

$$y=\frac{10±2\sqrt{23}i}{2\times 2}$$

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

$$y=\frac{10±2\sqrt{23}i}{4}$$

Réitigh an chothromóid y=\frac{10±2\sqrt{23}i}{4} nuair is ionann ± agus plus. Suimigh 10 le 2i\sqrt{23}?

$$y=\frac{10+2\sqrt{23}i}{4}$$

Roinn 10+2i\sqrt{23} faoi 4.

$$y=\frac{5+\sqrt{23}i}{2}$$

Réitigh an chothromóid y=\frac{10±2\sqrt{23}i}{4} nuair is ionann ± agus míneas. Dealaigh 2i\sqrt{23} ó 10.

$$y=\frac{-2\sqrt{23}i+10}{4}$$

Roinn 10-2i\sqrt{23} faoi 4.

$$y=\frac{-\sqrt{23}i+5}{2}$$

Tá dhá réiteach ann do y: \frac{5+i\sqrt{23}}{2} agus \frac{5-i\sqrt{23}}{2}. Cuir y in aonad \frac{5+i\sqrt{23}}{2} sa chothromóid eile x=-y+5 chun an réiteach comhfhreagrach do x a shásaíonn an dá chothromóid a fháil.

$$x=-\frac{5+\sqrt{23}i}{2}+5$$

Ansin cuir y in aonad \frac{5-i\sqrt{23}}{2} sa chothromóid eile x=-y+5 agus faigh réiteach chun an réiteach comhfhreagrach do x a shásaíonn an dá chothromóid a fháil.

$$x=-\frac{-\sqrt{23}i+5}{2}+5$$

Tá an córas réitithe anois.

$$x=-\frac{5+\sqrt{23}i}{2}+5,y=\frac{5+\sqrt{23}i}{2}\text{ or }x=-\frac{-\sqrt{23}i+5}{2}+5,y=\frac{-\sqrt{23}i+5}{2}$$