Question

If ax + by = a ^2 - b^2 and bx + ay = 0 then find the value of x + y
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Answer 1

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Answer 2

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Answer:

$ax + by = {a}^{2} - {b}^{2} ..........(i) \\ bx + ay = 0.........(ii) \\ \\ (i \times \: a)- (ii \times b) \\ \\ \: \: \: {a}^{2} x + aby = {a}^{3} - a {b}^{2} \\ - {b}^{2}x - aby = 0 \\-----------\\or,\: {a}^{2} x - {b}^{2} x = {a}^{3} - a {b}^{2} \\ or, \: x( {a}^{2} - {b}^{2} ) = a( {a}^{2} - {b}^{2} ) \\ or, \: x = \frac{( {a}^{2} - {b}^{2} ) }{( {a}^{2} - {b}^{2} ) } \\ or, \: x = 1 \\\\ x=1\: → (ii) \\\\ b \times 1 + ay = 0 \\ or, \: b + ay = 0 \\ or ,\: ay = - b \\ or,\: y = \frac { - b}{a}$

⁂(x,y) = ( 1 , -b/a)

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