Express the following equations in matrix form and solve them by method of reduction.

x + 3y = 2, 3x + 5y = 4

#### Solution

Matrix form of the given system of equations is

`[(1, 3),(3, 5)] [(x),(y)] = [(2),(4)]`

This is of the form AX = B,

where A = `[(1, 3),(3, 5)], "X" = [(x),(y)] "and B" = [(2),(4)]`

Applying R_{2} → R_{2} – 3R_{1}, we get

`[(1, 3),(0, -4)] [(x),(y)] = [(2),(-2)]`

Hence, the original matrix A is reduced to an upper triangular matrix.

∴ `[(x + 3y),(0 - 4y)] = [(2),(-2)]`

∴ By euality of matrices, we get

x + 3y = 2 ...(i)

– 4y = – 2 ...(ii)

From equation (ii),

y = `(1)/(2)`

Sustituting y = `(1)/(2)` in equation (i), we get

`x + 3/2` = 2

∴ x = `2 - (3)/(2) = (1)/(2)`

∴ x = `(1)/(2) "and y" =(1)/(2)` is the required soution.