For which values of a and b will the following pair of linear equations has infinitely many solutions ?
`x + 2y = 1`
` (a-b) x + (a + b ) y = a + b = -2`

Explanation

Given equations are
x + 2y - 1 = 0
(a - b)x + (a + b) y - (a + b - 2) = 0
Here `a_(1) = 1, b_(1) = 2, c_(1) = - 1`
`a_(2) = a - b, b_(2) = a + b, c_(2) = - (a + b - 2)`
For infinitely many solutions
`(a_(1))/(a_(2)) = (b_(1))/(b_(2)) = (c_(1))/(c_(2))`
`implies (1)/(a - b) = (2)/(a + b) = (-1)/(-(a + b - 2))`
Now `(1)/(a - b) = (2)/(a + b)` and `(1)/(a - b) = (-1)/(-(a + b - 2))`
implies 2a - 2b = a + b and a + b - 2 = a - b
implies a = 3b and 2b = 2 implies b = 1
`therefore` b = 1 and a = 3