Question

If two straight lines in x y -plane representing a pair of linear equations in two variables x and y overlap each other, then the pair of equations representing these lines will:
1. have infinite many solutions
2. have no possible solution
3. be inconsistent
4. have a unique solution

Answer 1

Correct Answer - Option 1 : have infinite many solutions

Concept:

Let us consider the pair of linear equations in two variables x and y 

⇒ a₁x + b₁y + c₁ = 0 ₂

⇒ a₂x + b₂y + c₂ = 0

Here, a₁, b_1, c₁, a₂ , b₂ , c₂  are all real numbers

Note that a₁² + b₁² ≠ 0 , a₂² + b₂² ≠ 0

Case - 1 

(a1 / a2) = (b1 / b2) = (c1 / c2) , then there will be infinitely many solutions

This type of equation called a dependent pair of linear equation in two variables .