Step-by-Step Solution
Key Concept: 1st equation: $bx + ay = 2ab$. 2nd equation: $ax - by = a^2 - b^2$. Multiply 1st by $b$ and 2nd by $a$: $b^2 x + ab y = 2ab^2$ and $a^2 x - ab y = a^3 - ab^2$. Add: $(a^2+b^2)x = a^3 + ab^2 = a(a^2+b^2) \Rightarrow x = a \Rightarrow y = b$.
$bx + ay = 2ab$ and $ax - by = a^2 - b^2$. [1.0 Mark]
Multiply 1st by $b$ and 2nd by $a$ and add: $(a^2 + b^2)x = a(a^2 + b^2) \Rightarrow x = a$. [1.0 Mark]
$b(a) + ay = 2ab \Rightarrow ay = ab \Rightarrow y = b$. Solution: $x = a, y = b$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Forming $bx + ay = 2ab$: 1.0 Mark
Solving $x = a$: 1.0 Mark
Solving $y = b$: 1.0 Mark
Correct Answer: