# Solve the following equations by the reduction method. x + 3y = 2, 3x + 5y = 4 - Mathematics and Statistics

Sum

Solve the following equations by the reduction method.

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

#### Solution

The given equations can be written in the matrix form as:

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

By R2 – 3R1, we get,

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

∴ [("x"+3"y"),(0-4"y")]=[(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.

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