# Solve the following equations by the reduction method. 3x – y = 1, 4x + y = 6 - Mathematics and Statistics

Sum

Solve the following equations by the reduction method.

3x – y = 1, 4x + y = 6

#### Solution

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

[(3,-1),(4,1)][("x"),("y")]=[(1),(6)]

By 4R1 and 3R2, we get,

[(12,-4),(12,3)][("x"),("y")]=[(4),(18)]

By R2 – R1, we get,

[(12,-4),(0,7)][("x"),("y")]=[(4),(14)]

∴ [(12"x"-4"y"),(0+7"y")]=[(4),(14)]

By equality of matrices,

12x − 4y = 4 ........(1)

7y = 14 .............(2)

From (2), y = 2

Substituting y = 2 in (1), we get,

12x − 8 = 4

∴ 12x = 12

∴ x = 1

Hence, x = 1, y = 2 is the required solution.

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