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)

Question

asked May 7, 2017 96.6k views

2 Answers

Lilydjwg · Answer 1 · 2017-05-10T06:36:54+0000

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)

Kvance · Answer 2 · 2017-05-11T11:42:02+0000

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.