Datrys {l}{x^2-4y^2=9}{y=7-3x}

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

Datrys ar gyfer x, y (complex solution)

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

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

Camau gan Ddefnyddio Amnewidiad a Fformiwla Cwadratig

Ystyriwch yr ail hafaliad. Ychwanegu 3x at y ddwy ochr.

$$y+3x=7$$

Tynnu 3x o ddwy ochr yr hafaliad.

$$y=-3x+7$$

Amnewid -3x+7 am y yn yr hafaliad arall, x^{2}-4y^{2}=9.

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

Sgwâr -3x+7.

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

Lluoswch -4 â 9x^{2}-42x+49.

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

Adio x^{2} at -36x^{2}.

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

Tynnu 9 o ddwy ochr yr hafaliad.

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

Mae’r hafaliad hwn yn y ffurf safonol: ax^{2}+bx+c=0. Amnewidiwch 1-4\left(-3\right)^{2} am a, -4\times 7\left(-3\right)\times 2 am b, a -205 am c yn y fformiwla gwadratig, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

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

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

Lluoswch -4 â 1-4\left(-3\right)^{2}.

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

Lluoswch 140 â -205.

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

Adio 28224 at -28700.

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

Cymryd isradd -476.

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

Lluoswch 2 â 1-4\left(-3\right)^{2}.

$$x=\frac{-168±2\sqrt{119}i}{-70}$$

Datryswch yr hafaliad x=\frac{-168±2\sqrt{119}i}{-70} pan fydd ± yn plws. Adio -168 at 2i\sqrt{119}.

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

Rhannwch -168+2i\sqrt{119} â -70.

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

Datryswch yr hafaliad x=\frac{-168±2\sqrt{119}i}{-70} pan fydd ± yn minws. Tynnu 2i\sqrt{119} o -168.

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

Rhannwch -168-2i\sqrt{119} â -70.

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

Mae dau ateb ar gyfer x: \frac{12}{5}-\frac{i\sqrt{119}}{35} a \frac{12}{5}+\frac{i\sqrt{119}}{35}. Amnewidiwch \frac{12}{5}-\frac{i\sqrt{119}}{35} am x yn yr hafaliad y=-3x+7 i ddod o hyd i'r ateb cyfatebol ar gyfer y sy'n bodloni'r ddau hafaliad.

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

Nawr, amnewidiwch \frac{12}{5}+\frac{i\sqrt{119}}{35} am x yn yr hafaliad y=-3x+7 a’i ddatrys i ganfod yr ateb cyfatebol ar gyfer y sy'n bodloni'r ddau hafaliad.

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

Mae’r system wedi’i datrys nawr.

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