Question 1199630: The number of pairs of integers (x,y) that satisfy both x^2 + y^2 ≤ 36 and y= -4 is...?
a) 4
b) 5
c) 6
d) 7
e) 8
This solution here: https://www.algebra.com/algebra/homework/Expressions-with-variables/Expressions-with-variables.faq.question.1064755.html
By Ms.Ikelyn didn't make sense to me if she could elaborate. Also, I couldn't find 9 in the multiple choice. Thank you so much!
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
These pairs of integers (x,y), satisfying the imposed conditions, are
(4,-4), (3,-4), (2,-4), (1,-4), (0,-4), (-1,-4), (-2,-4), (-3,-4), (-4,-4).
In all, there are 9 such pairs. ANSWER
This number " 9 " is not listed in the answers choice list, because this list in this post is  .
It MUST be there, but it is missed there due to the  made by the person who created this problem.
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In my previous post, to which you referred, I listed only first component x-values,
hoping that it is clear and enough; but in your case, as it turned out, it was not enough.
Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
x^2 + y^2 ≤ 36
x^2 + (-4)^2 ≤ 36
x^2 + 16 ≤ 36
x^2 ≤ 36-16
x^2 ≤ 20
sqrt(x^2) ≤ sqrt(20)
|x| ≤ sqrt(20)
|x| ≤ 4.4721 approximately
-4.4721 ≤ x ≤ 4.4721
-4 ≤ x ≤ 4 when x is an integer
The x coordinates span from -4 to 4, including both endpoints.
The x value is from the set {-4, -3, -2, -1, 0, 1, 2, 3, 4}
This constitutes 2*4+1 = 9 values of x, and hence there are 9 ordered pair integer solutions.
| (-4,-4) | (-3,-4) | (-2,-4) | | (-1,-4) | (0,-4) | (1,-4) | | (2,-4) | (3,-4) | (4,-4) |
Each pair has the y coordinate fixed to -4.
Unfortunately 9 isn't listed as a possible answer. Your teacher may have made a typo.
If I had to take a guess, it's possible your teacher wanted x to be nonzero.
If so then we'd ignore the solution (0,-4) and we'd go from 9 solutions to 9-1 = 8 solutions.
Again this is a guess of what your teacher wants. Ideally s/he should state all instructions and restrictions clearly.
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