Question

For the pair of equations kx + 2y = −4 and 5x + 10y = 8 to have infinitely [3] many solutions, the value of k should be 1. Is this statement true? Give
reasons

Answer 1

Given pairs of linear equations are :

➪ kx + 2y = – 4

➪ 5x + 10y = 8

In order to have infinitely many solutions, the following condition must be satisfied :

➪ a₁/a₂ = b₁/b₂ = c₁/c₂

When we compare kx + 2y = – 4 and 5x + 10y = 8 to ax + by + c = 0, we get :

➪ a₁ = k

➪ a₂ = 5

➪ b₁ = 2

➪ b₂ = 10

➪ c₁ = 4

➪ c₁ = – 8

Substituting and solving for k :

➪ a₁/a₂ = b₁/b₂

➪ k/5 = 2/10

Cross multiplying and solving :

➪ 10k = 5 × 2

➪ 10k = 10

➪ k = 10/10

➪ k = 1

Therefore, the value of k should be 1 for the pair of equations kx + 2y = – 4 and 5x + 10y = 8 to have infinitely many solutions.

So, the statement is true.