Solve the System by the Elimination Method or a Combination $x^{2}+4 x y+2 y^{2}=1$

Multiple Choice

Solve the system by the elimination method or a combination of the elimination and substitution methods.
- $x^{2}+4 x y+2 y^{2}=1$
$x^{2}-4 x y-2 y^{2}=1$

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