Solve the system of equations using elimination.
-$$\left\{ \begin{array} { l }
5 x ^ { 2 } - 2 y ^ { 2 } = 37 \
2 x ^ { 2 } + 2 y ^ { 2 } = 26
\end{array} \right.$$
A) $x = 3 , y = 2 ; x = - 3 , y = 2 ; x = 3 , y = - 2 ; x = - 3 , y = - 2$
B) $x = 3 , y = 2 ; x = 2 , y = 3 ; x = - 3 , y = - 2 ; x = - 2 , y = - 3$
C) $x = - 3 , y = - 2 ; x = - 2 , y = - 3$
D) $x = 3 , y = - 2 ; x = 3 , y = 2$

Question

Solve the system of equations using elimination.
-$$\left\{ \begin{array} { l } 
5 x ^ { 2 } - 2 y ^ { 2 } = 37 \
2 x ^ { 2 } + 2 y ^ { 2 } = 26
\end{array} \right.$$
A) $x = 3 , y = 2 ; x = - 3 , y = 2 ; x = 3 , y = - 2 ; x = - 3 , y = - 2$
B) $x = 3 , y = 2 ; x = 2 , y = 3 ; x = - 3 , y = - 2 ; x = - 2 , y = - 3$
C) $x = - 3 , y = - 2 ; x = - 2 , y = - 3$
D) $x = 3 , y = - 2 ; x = 3 , y = 2$

Quizplus · Accepted Answer

Adding the two equations eliminates $y^2$, resulting in $7x^2 = 63$, which simplifies to $x^2 = 9$, giving $x = 3$ or $x = -3$. Substituting $x$ back into one of the original equations allows solving for $y$, resulting in $y = 2$ or $y = -2$, thus providing all four solution pairs.

Solve the System of Equations Using Elimination {5x2−2y2=372x2+2y2=26\left\{ \begin{array} { l } 5 x ^ { 2 } - 2 y ^ { 2 } = 37 \\2 x ^ { 2 } + 2 y ^ { 2 } = 26\end{array} \right.{5x2−2y2=372x2+2y2=26​

Solve the System of Equations Using Elimination $\left\{ \begin{array} { l } 5 x ^ { 2 } - 2 y ^ { 2 } = 37 \\2 x ^ { 2 } + 2 y ^ { 2 } = 26\end{array} \right.$