Solve the following equations by the reduction method :
` x + 3y = 2, 3x + 5y = 4`.

Explanation

The given equations can be written in the matrix form as :
`{:((1,3),(3,5)):}{:((x),(y)):}={:((2),(4)):}`
By `R_(2) - 3R_(1)`, we get,
`{:((1,3),(0,-4)):}{:((x),(y)):}={:((2),(-2)):}`
`:. {:((x+3y),(0-4y)):}{:((2),(-2)):}`
By equality of matrices,
` x + 3y = 2 ` ....(1)
` -4y = -2` ....(2)
From (2), ` y = 1/2`
Substituting ` y = 1/2 ` in (1), we get ,
` x + 3/2 = 2 " " :. x = 2 - 3/2 = 1/2`
Hence, ` x = 1/2, y = 1/2` is the required solution.