Solve the following system of linear equations. :
` ( a - b) x + (a + b ) y = a ^(2) - 2ab - b ^(2) ` ,
` (a + b ) (x + y ) = a ^(2) + b ^(2)`.

Explanation

The given equations may be written as
` (a- b ) x + (a + b ) y = a ^(2) - 2ab - b ^(2)" " `… (i)
` (a+ b) x + (a + b ) y = a ^(2) + b ^(2) " " `… (ii)
Subtracting (i) from (ii), we get
` {(a + b ) - (a - b )} x = 2ab + 2b ^(2)`
`rArr 2bx = 2b (a + b ) rArr x = ( 2b(a + b ))/( 2b ) `
` rArr x = (a + b )`
Putting ` x= (a + b )` in (ii), we get
` (a + b ) ^(2) + (a + b) y = a ^(2) + b ^(2)`
`rArr (a + b ) y = (a ^(2) + b^(2)) - (a + b ) ^(2)`
`rArr (a + b ) y = (a ^(2) + b ^(2) ) - ( a ^(2) + b ^(2) + 2ab) `
`rArr ( a + b ) y = - 2ab rArr y = (-2ab)/( (a + b ))`
` therefore x = ( a + b ) and y = (- 2 ab )/( ( a+ b )) ` is the required solution.