Step-by-Step Solution
Key Concept: Expand 2nd: $(a + b)x + (a + b)y = a^2 + b^2$. Subtract from 1st: $[(a - b) - (a + b)]x = (a^2 - 2ab - b^2) - (a^2 + b^2) \Rightarrow -2bx = -2ab - 2b^2 = -2b(a + b) \Rightarrow x = a + b$. Substitute $x = a + b$ in 2nd: $(a + b)(a + b) + (a + b)y = a^2 + b^2 \Rightarrow (a + b)y = (a^2 + b^2) - (a^2 + 2ab + b^2) = -2ab \Rightarrow y = -\dfrac{2ab}{a + b}$.
Equation 2: $(a + b)x + (a + b)y = a^2 + b^2$. [1.0 Mark]
Subtract 2nd from 1st: $-2bx = -2ab - 2b^2 = -2b(a + b) \Rightarrow x = a + b$. [2.0 Marks]
Substitute $x = a + b$ in 2nd: $(a + b)^2 + (a + b)y = a^2 + b^2 \Rightarrow (a + b)y = -2ab \Rightarrow y = -\dfrac{2ab}{a + b}$. [2.0 Marks]
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🎯 Official CBSE Marking Scheme:
Writing equation 2 in standard form: 1.0 Mark
Subtracting equations to solve $x = a + b$: 2.0 Marks
Solving $y = -\dfrac{2ab}{a + b}$: 2.0 Marks
Correct Answer: