Question 996047
Let's check each answer choice.



Checking choice A. (1,4)


3x-5y >= 10
3*1-5*4 >= 10 ... plug in (x,y) = (1,4)
3-20 >= 10
-17 >= 10 ... false


since -17 >= 10 is false, this makes 3x-5y >= 10 false when (x,y)=(1,4). 
(1,4) is NOT a solution.


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Checking choice B. (6,-3)


3x-5y >= 10
3*6-5*(-3) >= 10 ... plug in (x,y) = (6,-3)
18+15 >= 10
33 >= 10 ... true


since 33 >= 10 is true, this makes 3x-5y >= 10 true when (x,y)=(6,-3). 
(6,-3) is a solution.

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Checking choice C. (-5, -2)


3x-5y >= 10
3*(-5)-5*(-2) >= 10 ... plug in (x,y) = (-5, -2)
-15+10 >= 10
-5 >= 10 ... false


since -5 >= 10 is false, this makes 3x-5y >= 10 false when (x,y)=(-5, -2). 
(-5, -2) is NOT a solution.

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Checking choice D. (2, 0)


3x-5y >= 10
3*(2)-5*(0) >= 10 ... plug in (x,y) = (2, 0)
6-0 >= 10
6 >= 10 ... false


since 6 >= 10 is false, this makes 3x-5y >= 10 false when (x,y)=(2, 0). 
(2, 0) is NOT a solution.


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Summary:


Only (6,-3) is a solution. So the only answer possible is <font color="red">B. (6, -3)</font>