SOLUTION: 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/h

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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(52777)   (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.

                        - - - Completed - - -


-------------


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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