Solve the System by the Elimination Method or a Combination $5 x^{2}+3 x y-5 y^{2}=-9$

Multiple Choice

Solve the system by the elimination method or a combination of the elimination and substitution methods.
- $5 x^{2}+3 x y-5 y^{2}=-9$
$x^{2}-x y-y^{2}=-5$

A) $\left\{(-1,2) ,(1,-2) ,\left(2 \mathrm{i} \sqrt{2}, \frac{\mathrm{i} \sqrt{2}}{2}\right) ,\left(-2 \mathrm{i} \sqrt{2},-\frac{\mathrm{i} \sqrt{2}}{2}\right) \right\}$

B) $\{(-1,-2) ,(1,2) ,(2 i,-i) ,(-2 i, i) \}$

C) $\{(-1,2) ,(1,-2) ,(2 i, i) ,(-2 i,-i) \}$

D) $\left\{(-1,-2) ,(1,2) ,\left(2 \mathrm{i} \sqrt{2},-\frac{\mathrm{i} \sqrt{2}}{2}\right) ,\left(-2 \mathrm{i} \sqrt{2}, \frac{\mathrm{i} \sqrt{2}}{2}\right) \right\}$