Réitigh {l}{x^2-4y^2=9}{y=7-3x}

$$\left. \begin{array} { l } { x ^ { 2 } - 4 y ^ { 2 } = 9 } \\ { y = 7 - 3 x } \end{array} \right.$$

Réitigh do x,y. (complex solution)

$$x=\frac{\sqrt{119}i}{35}+\frac{12}{5}\approx 2.4+0.311677489i\text{, }y=-\frac{3\sqrt{119}i}{35}-\frac{1}{5}\approx -0.2-0.935032467i$$

$$x=-\frac{\sqrt{119}i}{35}+\frac{12}{5}\approx 2.4-0.311677489i\text{, }y=\frac{3\sqrt{119}i}{35}-\frac{1}{5}\approx -0.2+0.935032467i$$

Céimeanna ag Baint Úsáid as Ionadú agus an bhFoirme Chearnach

Cuir an dara cothromóid san áireamh. Cuir 3x leis an dá thaobh.

$$y+3x=7$$

Bain 3x ón dá thaobh den chothromóid.

$$y=-3x+7$$

Cuir y in aonad -3x+7 sa chothromóid eile, x^{2}-4y^{2}=9.

$$x^{2}-4\left(-3x+7\right)^{2}=9$$

Cearnóg -3x+7.

$$x^{2}-4\left(9x^{2}-42x+49\right)=9$$

Méadaigh -4 faoi 9x^{2}-42x+49.

$$x^{2}-36x^{2}+168x-196=9$$

Suimigh x^{2} le -36x^{2}?

$$-35x^{2}+168x-196=9$$

Bain 9 ón dá thaobh den chothromóid.

$$-35x^{2}+168x-205=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir 1-4\left(-3\right)^{2} in ionad a, -4\times 7\left(-3\right)\times 2 in ionad b, agus -205 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-168±\sqrt{168^{2}-4\left(-35\right)\left(-205\right)}}{2\left(-35\right)}$$

Cearnóg -4\times 7\left(-3\right)\times 2.

$$x=\frac{-168±\sqrt{28224-4\left(-35\right)\left(-205\right)}}{2\left(-35\right)}$$

Méadaigh -4 faoi 1-4\left(-3\right)^{2}.

$$x=\frac{-168±\sqrt{28224+140\left(-205\right)}}{2\left(-35\right)}$$

Méadaigh 140 faoi -205.

$$x=\frac{-168±\sqrt{28224-28700}}{2\left(-35\right)}$$

Suimigh 28224 le -28700?

$$x=\frac{-168±\sqrt{-476}}{2\left(-35\right)}$$

Tóg fréamh chearnach -476.

$$x=\frac{-168±2\sqrt{119}i}{2\left(-35\right)}$$

Méadaigh 2 faoi 1-4\left(-3\right)^{2}.

$$x=\frac{-168±2\sqrt{119}i}{-70}$$

Réitigh an chothromóid x=\frac{-168±2\sqrt{119}i}{-70} nuair is ionann ± agus plus. Suimigh -168 le 2i\sqrt{119}?

$$x=\frac{-168+2\sqrt{119}i}{-70}$$

Roinn -168+2i\sqrt{119} faoi -70.

$$x=-\frac{\sqrt{119}i}{35}+\frac{12}{5}$$

Réitigh an chothromóid x=\frac{-168±2\sqrt{119}i}{-70} nuair is ionann ± agus míneas. Dealaigh 2i\sqrt{119} ó -168.

$$x=\frac{-2\sqrt{119}i-168}{-70}$$

Roinn -168-2i\sqrt{119} faoi -70.

$$x=\frac{\sqrt{119}i}{35}+\frac{12}{5}$$

Tá dhá réiteach ann do x: \frac{12}{5}-\frac{i\sqrt{119}}{35} agus \frac{12}{5}+\frac{i\sqrt{119}}{35}. Cuir x in aonad \frac{12}{5}-\frac{i\sqrt{119}}{35} sa chothromóid eile y=-3x+7 chun an réiteach comhfhreagrach do y a shásaíonn an dá chothromóid a fháil.

$$y=-3\left(-\frac{\sqrt{119}i}{35}+\frac{12}{5}\right)+7$$

Ansin cuir x in aonad \frac{12}{5}+\frac{i\sqrt{119}}{35} sa chothromóid eile y=-3x+7 agus faigh réiteach chun an réiteach comhfhreagrach do y a shásaíonn an dá chothromóid a fháil.

$$y=-3\left(\frac{\sqrt{119}i}{35}+\frac{12}{5}\right)+7$$

Tá an córas réitithe anois.

$$y=-3\left(-\frac{\sqrt{119}i}{35}+\frac{12}{5}\right)+7,x=-\frac{\sqrt{119}i}{35}+\frac{12}{5}\text{ or }y=-3\left(\frac{\sqrt{119}i}{35}+\frac{12}{5}\right)+7,x=\frac{\sqrt{119}i}{35}+\frac{12}{5}$$