Advertisement Remove all ads

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

Advertisement Remove all ads

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.

  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×