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KCET2026MathematicsDeterminants

The system of equations x + 2y = 3 and 2x + 3y = 3 has

Options

  1. ANo solution
  2. BUnique solution
  3. CInfinite solutions
  4. DOnly two solutions

Correct answer

B. Unique solution

Step-by-step solution

The given system of equations is: x + 2y = 3 2x + 3y = 3 Comparing with the standard form a₁x + b₁y = c₁ and a₂x + b₂y = c₂ , we have: a₁ a₂ = 1 2 b₁ b₂ = 2 3 Since a₁ a₂ b₁ b₂ , the lines intersect at a single point. Therefore, the system of equations has a unique solution. Answer: Unique solution

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