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Solve: `a x+b y=a-b , b x-a y=a+b` |
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Answer» The given equations may be written as ` a x + by = a - b " " `… (i) ` bx - ay = a + b " " `… (ii) Multiplying (i) by a and (ii) by b and adding the results, we get `(a ^(2) + b ^(2)) x = (a ^(2) + b ^(2)) rArr x = 1 ` Putting ` x = 1 ` in (i) , we get ` ( a xx 1 ) + by = a- b ` ` rArr a + by = a - b ` ` rArr by = - b rArr y = (-b)/(b) = - 1 ` Hence, ` x = 1 and y = - 1`. |
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