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

Multiple Choice

Solve the system by the elimination method or a combination of the elimination and substitution methods.
- $x^{2}-x y+y^{2}=3$
$2 x^{2}+x y+2 y^{2}=12$

A) $\{(2,1) ,(1,2) \}$
B) $\{(1,0) ,(-1,0) \}$
C) $\{(2,1) ,(-2,-1) ,(1,2) ,(-1,-2) \}$
D) $\{(2,0) ,(-2,0) ,(1,0) ,(-1,0) \}$