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,
--------(1)
----------(2)
By adding the above equations,
We get,
![2x^2=10](https://tex.z-dn.net/?f=2x%5E2%3D10)
![x^2=5](https://tex.z-dn.net/?f=x%5E2%3D5)
![x=\pm \sqrt{5}](https://tex.z-dn.net/?f=x%3D%5Cpm%20%5Csqrt%7B5%7D)
When x = √5
Then, from the equation (1),
![5 + y^2=9](https://tex.z-dn.net/?f=5%20%2B%20y%5E2%3D9)
![y^2=4](https://tex.z-dn.net/?f=y%5E2%3D4)
![y=\pm 2](https://tex.z-dn.net/?f=y%3D%5Cpm%202)
Hence, the solutions are (√5, 2) and (√5,-2)
Again if x = -√5,
By equation (1),
![5+y^2=9](https://tex.z-dn.net/?f=5%2By%5E2%3D9)
![y^2=4](https://tex.z-dn.net/?f=y%5E2%3D4)
![y=\pm 2](https://tex.z-dn.net/?f=y%3D%5Cpm%202)
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.