Q. 84.0( 4 Votes )

If the system of A. a = 2b

B. b = 2a

C. a + 2b = 0

D. 2a + b = 0

Answer :

Given:

Equation 1: 2x + 3y = 7


Equation 2: 2ax + (a + b)y = 28


Both the equations are in the form of :


a1x + b1y = c1 & a2x + b2y = c2 where


a1 & a2 are the coefficients of x


b1 & b2 are the coefficients of y


c1 & c2 are the constants


For the system of linear equations to have infinitely many solutions we must have


………(i)


According to the problem:


a1 = 2


a2 = 2a


b1 = 3


b2 = (a + b)


c1 = 7


c2 = 28


Putting the above values in equation (i) and solving the extreme left and extreme right portion of the equality we get the value of a



14a = 56 a = 4


We now put the value of a and solve for b


a + b = 12 b = 8


So b = 2a


The correct relationship between a & b for which the system of equations has infinitely many solution is b = 2a

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