If simultaneous system of equations has infinitely many solutions then the pair of linear equation is said to be :

Correct option is C

The correct answer is: (c) Dependent

A system of simultaneous linear equations is said to be dependent if it has infinitely many solutions. This means the two equations are not independent; instead, they represent the same line, overlapping entirely. Such systems are also consistent, as they do have solutions, but the term dependent emphasizes the specific nature of the relationship between the equations.
A dependent system arises when the two equations are proportional, i.e., a1/a2 = b1/b2 = c1/c2​​, where the equations are written as a1x+b1y+c1=0a_1x + b_1y + c_1 = 0a1​x+b1​y+c1​=0 and a2x+b2y+c2=0a_2x + b_2y + c_2 = 0a2​x+b2​y+c2​=0.

A consistent system can either be:

• Independent (with a unique solution)
• Dependent (with infinitely many solutions)

In dependent systems, every solution of one equation is also a solution of the other, as they represent the same line.

Additional Information:

• Inconsistent Systems: A system with no solution (e.g., parallel lines).
• Consistent Systems: Systems that have at least one solution, which includes:
  • Independent Systems: A consistent system where the two equations intersect at exactly one point.
  • Dependent Systems: A consistent system with infinitely many solutions