Solve the system of equations using elimination.
-$$\left\{ \begin{array} { l }
2 x ^ { 2 } - 4 y ^ { 2 } = 2 \
3 x ^ { 2 } + 2 y ^ { 2 } = 35
\end{array} \right.$$
A) x = 3, y = -2; x = 3, y = 2
B) x = -3, y = -2; x = -2, y = -3
C) x = 3, y = 2; x = -3, y = 2 ; x = 3, y = -2; x = -3, y = -2
D) x = 3, y = 2; x = 2, y = 3; x = -3, y = -2; x = -2, y = -3

Question

Solve the system of equations using elimination.
-$$\left\{ \begin{array} { l } 
2 x ^ { 2 } - 4 y ^ { 2 } = 2 \
3 x ^ { 2 } + 2 y ^ { 2 } = 35
\end{array} \right.$$
A) x = 3, y = -2; x = 3, y = 2
B) x = -3, y = -2; x = -2, y = -3
C) x = 3, y = 2; x = -3, y = 2 ; x = 3, y = -2; x = -3, y = -2
D) x = 3, y = 2; x = 2, y = 3; x = -3, y = -2; x = -2, y = -3

Quizplus · Accepted Answer

To solve the system of equations using elimination, we add the two equations to eliminate $y^2$. Adding them gives $5x^2 = 37$, leading to $x^2 = \frac{37}{5}$. Solving for $x$, we get $x = \pm \sqrt{\frac{37}{5}}$. Substituting $x$ back into one of the original equations allows us to solve for $y$, resulting in four possible combinations of $x$ and $y$: $x = 3, y = 2$; $x = -3, y = 2$; $x = 3, y = -2$; $x = -3, y = -2$.

Solve the System of Equations Using Elimination {2x2−4y2=23x2+2y2=35\left\{ \begin{array} { l } 2 x ^ { 2 } - 4 y ^ { 2 } = 2 \\3 x ^ { 2 } + 2 y ^ { 2 } = 35\end{array} \right.{2x2−4y2=23x2+2y2=35​

Solve the System of Equations Using Elimination $\left\{ \begin{array} { l } 2 x ^ { 2 } - 4 y ^ { 2 } = 2 \\3 x ^ { 2 } + 2 y ^ { 2 } = 35\end{array} \right.$