Question

Find the value of k for which the system of linear equations has an infinite number of solutions. 

2x + 3y=9, 

6x + (k – 2)y =(3k – 2)

Answer 1

The given pair of linear equations are 

2x + 3y – 9 = 0 ……(i) 

6x + (k – 2)y – (3k – 2) = 0 ……(ii) 

Which is of the form a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, 

where a₁ = 2, b₁ = 3, c₁ = -9, a₂ = 6, b₂ = k – 2 and c₂ = -(3k – 2) 

For the given pair of linear equations to have infinitely many solutions, we must have