Question

The answer is D but I don't understand how that is.
Please explain?
I'm studying for my SAT

If x and y are positive integers, what are all the solutions (x,y) of the equation (3 times x) + (2 times y) = 11?


(A) (1,4) only
(B) (1,3) only
(C) (1,4) and (2,2)
(D) (1,4) and (3,1)
(E) (2,2) and (3,1)

Answer 1

\[3x + 2y = 11\]

Answer 2

If you plug in the points given in options then you can easily check whether they are valid points or not..

Answer 3

Like first point of your D part is (1,4) here x = 1 and y is also 4..

So; in original equation, plug in x = 1, and y = 4:

\[LHS : \; \; 3(1) + 2(4) = 3 + 8 = 11 = RHS\]

Answer 4

So, (1,4) is a valid point. Similarly you can check for other points..

Answer 5

Are you getting??

Answer 6

With (1,4) options are A, C and D, see you have successfully eliminated two option which are B and E..
So, from A, C and D, you have to eliminate two more and that you can do by checking for point (3,1)..

Answer 7

And please don't make me feel like I am talking to myself here...

Answer 8

Sorryyyyy I was on another tab but I think I understand now ^-^ thank you

Answer 9

If you think so, then it is alright.. :)