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

Answer: all of the above

Explanation:

This is a system of equations. You have different ways to solve these: substitution, elimination or graphing

Using elimination seems the easiest to me.

You will eliminate the "y"

`x^2 + y^2=9\\+ x^2-y^2=1\\= 2x^2 =10`

Now solve
`2x^2=10`

Divide by 2

`x^2=5`

Take the square root. Remember when you take the square root you get a positive answer and a negative answer

`x=√(5)` and
`x=-√(5)`

Now, plug that back in to one of the original equations to find y.

`(√(5) )^2-y^2=1`

`5-y^2=1`

subtract 5

`-y^2=-4`

Divide by -1

`y^2=4`

Square root (and remember the positive/negative)

`y=2` and
`y=-2`

So:
`(√(5) , 2),(√(5), -2)`

BUT you still need to plug in
`-√(5)`

`(-√(5) )^2-y^2=1`

`5-y^2=1`

`-y^2=-4`

`y^2=4`

`y=2` and
`y=-2`

So:
`(-√(5) , 2),(-√(5), -2)`

The correct answer is all 4 of those choices!