Find all real solutions to the system of equations using the addition method.
-$\begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 100 \
x ^ { 2 } - y ^ { 2 } = 100
\end{array}$
A)(-10, 0), (-10, 10)
B)(10, 0), (-10, 0)
C)(10, 10), (-10, 10)
D)(10, 0), (10, 10)

Question

Find all real solutions to the system of equations using the addition method.
-$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 100 \
x ^ { 2 } - y ^ { 2 } = 100
\end{array}$
A)(-10, 0), (-10, 10)
B)(10, 0), (-10, 0)
C)(10, 10), (-10, 10)
D)(10, 0), (10, 10)

Quizplus · Accepted Answer

Adding the two equations eliminates $y^2$, resulting in $2x^2 = 200$, which simplifies to $x^2 = 100$. Solving for $x$ gives $x = 10$ and $x = -10$. Substituting $x = 10$ into the first equation, we find $y = 0$, and similarly for $x = -10$, $y = 0$. Thus, the solutions are $(10, 0)$ and $(-10, 0)$.

Find All Real Solutions to the System of Equations Using x2+y2=100x2−y2=100\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 100 \\x ^ { 2 } - y ^ { 2 } = 100\end{array}x2+y2=100x2−y2=100​

Find All Real Solutions to the System of Equations Using $\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 100 \\x ^ { 2 } - y ^ { 2 } = 100\end{array}$