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) we get:


…(ii)



To obtain the value of a & b we need to solve the above equality. First we solve the extreme left and extreme right of the equality to obtain the value of a.


2a*7 = 2*28 14a = 56 a = 4


After obtaining the value of a we again solve the extreme left and middle portion of the equality (ii)


2*(4 + b) = 3*2*4 b + 4 = 12 b = 8


The value of a & b for which the system of equations has infinitely many solution is a = 4 & b = 8



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