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) $\{(2,0),(-2,0),(1,0),(-1,0)\}$

Question

Quizplus · Accepted Answer

To solve the system, subtract the first equation from the second to eliminate $xy$, resulting in $x^2 + y^2 = 9$, which represents a circle. Solving the system involves finding points that satisfy both equations, leading to four solutions: $(2,1), (-2,-1), (1,2), (-1,-2)$.

Solve the System by the Elimination Method or a Combination x2−xy+y2=3x^{2}-x y+y^{2}=3x2−xy+y2=3

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