if the pair of lines 2x+3y+7=0 and ax+by+14=0 are coincident lines then what is the value of ‘a’ and ‘b’ are respectively equal to

There are many ways of doing this que 

As we can see in the que. if we multiply given equation by 2 we see the constant coefficients of both the equation became equal. And hence coefficients of x and y will also be equal for both the lines to be coincident.

i.e. a=4.   &     b=6.

2^nd way

First of all we find two points from the given equations at x is equal to zero and at Y is equal to zero.

i.e. at x=0

2*0+3y=-7

Y= -7/3.  (0,-7/3)

N at y=0

2x=-7

X=-7/2.   i.e. (-7/2,0)

further these points will satisfy the given second equation of coincident line

And we'll get values of a and b .

i.e.

At (0,-7/3)

-7b/3 = -14.       b = 6

At (-7/2,0)

-7a/2= -14.         a = 4

 

There are many more ways of doing the question. 

Thank you