For a unique solution, a₁/a₂ ≠ b₁/b₂. Here, 4/2 ≠ p/2, which simplifies to 2 ≠ p/2, giving p ≠ 4. Thus, a unique solution exists for all real values of p except 4.
Ganita Manjari Class 9 Maths part 2 Chapter 13 Solutions
Class 9 Ganita Manjari Part 2 Chapter 13 Page 121 Question Answer
A pair of linear equations has a unique solution if and only if the ratio of the coefficients of x and y are not equal, that is, a₁/a₂ ≠ b₁/b₂. From the equations 4x + py + 8 = 0 and 2x + 2y + 2 = 0, this requires 4/2 ≠ p/2. Simplifying yields 2 ≠ p/2, which means p ≠ 4. Therefore, the system has a unique solution for all real values of p except 4.
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