The pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines if

a. a=b b. 3a = 2b c. 2a = 3b d. ab = 6

Given system of equations is: ax+2y=7 and 3x+by=16.

They can be rewritten as:

ax + 2y - 7 = 0 and

3x + by - 16 = 0

 We know that, for the given system of equations to have parallel lines or inconsistent solution, = , i.e., 

=

⇒ ab = 6

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d. ab = 6

in parallel lines , 1=2 but not =3 

a/3 = 2/b not = 7/16

a/3 = 7/16             2/b = 7/16 

a = 21/16                   b = 32/7

ab = 21/16 *32/7 = 6

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