Find all real solutions to the system of equations using the addition method.
-$\begin{array} { l }
3 x ^ { 2 } - 2 y ^ { 2 } = - 6 \
2 x ^ { 2 } + 4 y ^ { 2 } = 44
\end{array}$
A)(2, -3), (2, 3)
B)(-2, -3), (-3, -2)
C)(2, 3), (3, 2), (-2, -3), (-3, -2)
D)(2, 3), (-2, 3), (2, -3), (-2, -3)

Question

Find all real solutions to the system of equations using the addition method.
-$\begin{array} { l } 
3 x ^ { 2 } - 2 y ^ { 2 } = - 6 \
2 x ^ { 2 } + 4 y ^ { 2 } = 44
\end{array}$
A)(2, -3), (2, 3)
B)(-2, -3), (-3, -2)
C)(2, 3), (3, 2), (-2, -3), (-3, -2)
D)(2, 3), (-2, 3), (2, -3), (-2, -3)

Quizplus · Accepted Answer

To solve the system, add the two equations to eliminate $y^2$: $3x^2 - 2y^2 + 2x^2 + 4y^2 = -6 + 44$, simplifying to $5x^2 = 38$, or $x^2 = \frac{38}{5}$. Solving for $x$, we get $x = \pm\sqrt{\frac{38}{5}}$, which simplifies to $x = \pm\sqrt{7.6}$, or $x = \pm2$. Substituting $x = 2$ into the first equation gives $3(2)^2 - 2y^2 = -6$, leading to $12 - 2y^2 = -6$, and solving for $y$ gives $y = \pm3$. Similarly, substituting $x = -2$ and solving for $y$ also gives $y = \pm3$. Therefore, the solutions are $(2, 3), (-2, 3), (2, -3), (-2, -3)$.

Find All Real Solutions to the System of Equations Using 3x2−2y2=−62x2+4y2=44\begin{array} { l } 3 x ^ { 2 } - 2 y ^ { 2 } = - 6 \\2 x ^ { 2 } + 4 y ^ { 2 } = 44\end{array}3x2−2y2=−62x2+4y2=44​

Find All Real Solutions to the System of Equations Using $\begin{array} { l } 3 x ^ { 2 } - 2 y ^ { 2 } = - 6 \\2 x ^ { 2 } + 4 y ^ { 2 } = 44\end{array}$