Step-by-Step Solution
Key Concept: Multiply 1st by $a$: $a^2 x + ab y = a^2 - ab$. Multiply 2nd by $b$: $b^2 x - ab y = ab + b^2$. Add: $(a^2+b^2)x = a^2+b^2 \Rightarrow x = 1$. Substitute $x = 1$: $a + by = a - b \Rightarrow by = -b \Rightarrow y = -1$.
Multiply 1st by $a$ and 2nd by $b$ and add: $(a^2 + b^2)x = a^2 + b^2 \Rightarrow x = 1$. [1.5 Marks]
Substitute $x = 1$ in 1st: $a(1) + by = a - b \Rightarrow by = -b \Rightarrow y = -1$. Solution: $x = 1, y = -1$. [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Eliminating $y$ to solve $x = 1$: 1.5 Marks
Substituting $x = 1$ to solve $y = -1$: 1.5 Marks
Correct Answer: