SravnaTestPrep wrote:

If \(ax + by = 17\) ,

\(2ax + 3by = 43\)

and \(3x =2y\), which of the following is a possible value of \(a+b\) if a and b are integers?

A. 6

B. 10

C. 14

D. 18

E. 20

Too many variables! I will try to look at the big picture here.

We have two equations:

\(ax + by = 17\) ,

\(2ax + 3by = 43\)

Twice of (ax + by) will be 34 so we get that 'by' must be 43 - 34 = 9

If by = 9, ax must be 17 - 9 = 8

Now, x/y = 2/3

ax/by = (a/b)*(2/3) = 8/9

So a/b = 4/3

Since a and b are integers, many such solutions are possible: a = 4, b = 3 OR a = 8, b = 6 etc. a+b will be 7/14/21...

Answer (C)

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