Answer: The solution of the given system is,
(√5, 2)
(√5, -2)
(-√5, 2)
(-√5, -2)
Step-by-step explanation:
Here, the given system of equation is,
\(x^2+y^2=9\) --------(1)
\(x^2-y^2=1\) ----------(2)
By adding the above equations,
We get,
\(2x^2=10\)
\(x^2=5\)
\(x=\pm \sqrt{5}\)
When x = √5
Then, from the equation (1),
\(5 + y^2=9\)
\(y^2=4\)
\(y=\pm 2\)
Hence, the solutions are (√5, 2) and (√5,-2)
Again if x = -√5,
By equation (1),
\(5+y^2=9\)
\(y^2=4\)
\(y=\pm 2\)
Hence, the solutions are (-√5,2) and (-√5,-2)
Thus, the all solutions of the given system are (√5,2), (√5,-2), (-√5,2) and (-√5,-2)
⇒ All options are correct.
