The method for solving this has slipped my mind. Can someone help me please?

x^2 + y^2 = 17

x + y = -3

I was thinking of squaring the bottom one then using elimination, but I got the wrong answer doing that =/.

how about you say y=-(x+3)

put that into equation 1

...

profit?

I would solve for y:

x + y = -3 => y = x - 3

and plug into the other equation:

x^2 + (x-3)^2 = 17
x^2 + x^2 -6x + 9 = 17
2x^2 - 6x - 8 = 0
x^2 -3x - 4 = 0
(x - 4)(x + 1) = 0
x = 4, x = -1

and then plug back into first equation
y = 1, y = -4

take the bottom one and solve it for either variable (I'll solve for y):
x + y = -3
y = -3 - x
now take this result and replace y in the first equation with it:

x^2 + y^2 = 17

x^2 +( -3 - x)^2 = 17

expand that bracket

x^2 + x^2 + 6x + 9 = 17

2x^2 + 6x + 9 = 17

2x^2 + 6x - 8 = 0

2 (x^2 + 3x - 4) = 0
2 (x + 4)(x - 1) = 0
(x + 4)(x - 1) = 0
x = -4, x = 1

now plug those into the bottom equation
-4 + y = -3 , 1 + y = -3
y = 1, y = -4
so {-4,1} and {1,-4}

Er.. I completely forgot about that option haha. Thanks guys, I'm math retarded at the moment because of a long break from school :).