If the system of equations
2x + 3y = 7
2ax + (a + b)y = 28
has infinitely many solutions, then
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