Find all real solutions to the system of equations using the addition method.
-$\begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 80 \
x ^ { 2 } - y ^ { 2 } = - 48
\end{array}$
A)(4, -8), (4, 8)
B)(4, 8), (-4, 8), (4, -8), (-4, -8)
C)(4, 8), (8, 4), (-4, -8), (-8, -4)
D)(-4, -8), (-8, -4)

Question

Find all real solutions to the system of equations using the addition method.
-$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 80 \
x ^ { 2 } - y ^ { 2 } = - 48
\end{array}$
A)(4, -8), (4, 8)
B)(4, 8), (-4, 8), (4, -8), (-4, -8)
C)(4, 8), (8, 4), (-4, -8), (-8, -4)
D)(-4, -8), (-8, -4)

Quizplus · Accepted Answer

Adding the two equations eliminates $y^2$, resulting in $2x^2 = 32$, or $x^2 = 16$, giving $x = \pm 4$. Substituting $x = 4$ and $x = -4$ into the original equations allows solving for $y$, resulting in $y = \pm 8$. Thus, all combinations of $(\pm 4, \pm 8)$ are solutions.

Find All Real Solutions to the System of Equations Using x2+y2=80x2−y2=−48\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 80 \\x ^ { 2 } - y ^ { 2 } = - 48\end{array}x2+y2=80x2−y2=−48​

Find All Real Solutions to the System of Equations Using $\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 80 \\x ^ { 2 } - y ^ { 2 } = - 48\end{array}$