For which value(s) of $p$ does the pair of equations given below have a unique solution?
$4x + py + 8 = 0$
$2x + 2y + 2 = 0$
Step-by-Step Solution
Key Concept: Unique solution condition: $\dfrac{a_1}{a_2} <br>eq \dfrac{b_1}{b_2}$.
Here $a_1=4, b_1=p$ and $a_2=2, b_2=2$. [0.5 Mark]
For unique solution: $\dfrac{4}{2}
eq \dfrac{p}{2} \Rightarrow 2
eq \dfrac{p}{2} \Rightarrow p
eq 4$. [1.0 Mark]
Thus, the pair of equations will have a unique solution for all values of $p$ except $p = 4$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Stating unique solution condition: 0.5 Mark
Solving inequality $\dfrac{4}{2}
eq \dfrac{p}{2}$: 1.0 Mark
Concluding $p
eq 4$: 0.5 Mark
Correct Answer: