Question

which of the following is a point in the intersection of x^2 + y^2 < 4 and x - 3y < -3?
(a) (0, 1)
(b) (1, -1)
(c) (1, 0)
(d) (-1, 1)
(e) (0, 0)

Answer 1

Good question!
We have a circle with radius = 2
and what else? what is the second thing?

Answer 2

why not sketch it?

Answer 3

The second inequality is tricky
x - 3y < -3
(1/3)x - y < -1
y > (1/3)x + 1

Answer 4

Not sure exactly where the line goes yet.

Answer 5

I've drawn it badly, the y-intercept is 1, the x-intercept is -3. So it should cross the circle at positive y.

Answer 6

You there?

Answer 7

yeah

Answer 8

Now, the question is pretty easy I think.
(0,1) won't do b/c it doesn't satisfy y > (1/3)x + 1
it satisfies = but not >

Answer 9

Only -1, 1 looks possible.

Answer 10

And I should've said, they are all inside the circle.

Answer 11

ok thank you so much

Answer 12

yw