values of a and b for which the system of linear equations has an infinite number of solutions: (2a – 1) x + 3y = 5, 3x + (b – 1)y = 2.

Question

Find the values of a and b for which the system of linear equations has an infinite number of solutions: 

(2a – 1) x + 3y = 5, 

3x + (b – 1)y = 2.

Answer 1

The given system of equations can be written as 

(2a – 1) x + 3y = 5 

⇒(2a – 1) x + 3y – 5 = 0 ….(i) 

and 3x + (b – 1)y = 2 

⇒3x + (b – 1)y – 2 = 0 ….(ii) 

These equations are of the following form:

a₁x+b₁y+c₁ = 0, a₂x+b₂y+c₂ = 0 

where, a₁ = (2a – 1), b₁= 3, c₁ = -5 and a₂ = 3, b₂ = (b – 1), c₂ = -2 

For an infinite number of solutions, we must have: