1.

Solve the following pair of linear equations 2(ax-by) + (a + 4b) = 0 2(bx + ay) + (b-40 = 0

Answer» The given equations may be written as
` 2ax - 2by = -a - 4b " " `… (i)
` 2bx + 2ay = 4a - b " " `… (ii)
Multiplying (i) by a and (ii) by b and adding , we get
` ( 2 a ^(2) + 2 b ^(2)) x = ( - a ^(2) - b ^(2))`
` rArr 2 (a ^(2) + b (2)) x = - (a ^(2) + b ^(2)) rArr x = (-1)/(2)`
Putting ` x = (-1)/(2) ` in (i), we get
` 2a xx ((-1)/(2)) - 2 by = - a - 4 b `
` rArr - a - 2by = - a - 4 b `
` rArr 2by = 4 b rArr y = ( 4 b )/( 2 b ) = 2 `
Hence, ` x = (-1)/(2) and y = 2 `


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