Question

X2 + y2 = 9

x2 - y2 = 1

Select all of the following that are solutions to the system shown.

(√5, 2)
(√5, -2)
(-√5, 2)
(-√5, -2)

Answer 1

I hope this helps you

x^2+y^2=9


x^2-y^2=1

x^2+y^2+x^2-y^2=9+1

2x^2=10

x^2=5

x= square root of 5


5+y^2=9

y^2=4

y=2


(square root of 5,2)

Answer 2

Answer: The solution of the given system is,

(√5, 2)

(√5, -2)

(-√5, 2)

(-√5, -2)

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 √(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.