Find all real solutions to the system of equations using the addition method.
-$\begin{array} { c }
2 x ^ { 2 } + y ^ { 2 } = 17 \
3 x ^ { 2 } - 2 y ^ { 2 } = - 6
\end{array}$
A)(2, -3), (-2, 3)
B)(1, 3), (1, -3), (-1, 3), (-1, -3)
C)(1, 3), (-1, -3)
D)(2, 3), (2, -3), (-2, 3), (-2, -3)

Question

Find all real solutions to the system of equations using the addition method.
-$\begin{array} { c } 
2 x ^ { 2 } + y ^ { 2 } = 17 \
3 x ^ { 2 } - 2 y ^ { 2 } = - 6
\end{array}$
A)(2, -3), (-2, 3)
B)(1, 3), (1, -3), (-1, 3), (-1, -3)
C)(1, 3), (-1, -3)
D)(2, 3), (2, -3), (-2, 3), (-2, -3)

Quizplus · Accepted Answer

By adding and subtracting the equations, we find the values of $x^2$ and $y^2$, leading to the solutions for $x$ and $y$.

Find All Real Solutions to the System of Equations Using 2x2+y2=173x2−2y2=−6\begin{array} { c } 2 x ^ { 2 } + y ^ { 2 } = 17 \\3 x ^ { 2 } - 2 y ^ { 2 } = - 6\end{array}2x2+y2=173x2−2y2=−6​

Find All Real Solutions to the System of Equations Using $\begin{array} { c } 2 x ^ { 2 } + y ^ { 2 } = 17 \\3 x ^ { 2 } - 2 y ^ { 2 } = - 6\end{array}$