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11. Solve by cross multiplication: x+y = a+b and ax-by= a^2 - b^2.

Answer»

→ X + y - (a + B) = 0

→ AX - by - (a² - b²) = 0

\mathsf{= \frac{x}{ - ( {a}^{2} - {b}^{2}) - b(a + b)}} \\ \mathsf{= \frac{x}{ - {a}^{2} + {b}^{2} - ab - {b}^{2} }} \\ \mathsf{= \frac{x}{ - a(a + b)}}

\mathsf{ = \frac{ - y}{ - ( {a}^{2} - {b}^{2} ) + a(a + b) }} \\ \mathsf{= \frac{ - y}{ - {a}^{2} + {b}^{2} + {a}^{2} + ab }} \\ \mathsf{= \frac{ - y}{b(a + b)}}

\mathsf{ = \frac{1}{ - b - a}} \\ \mathsf{= \frac{1}{- (a + b)}}

______________________________

\mathsf{\frac{x}{-a(a+b)} = \frac{-y}{b(a+b)} = \frac{1}{-(a + b)}} \\ \mathsf{x = \frac{-a(a+b)}{-(a+b)} = a} \\ \mathsf{-y = \frac{b(a+b)}{-(a+b)} = b}

x = a & y = b


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