Question

Solve the following equations by the reduction method.

2x + y = 5, 3x + 5y = – 3

Answer 1

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

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

By 2R₂ , we get,

`[(2,1),(6,10)][("x"),("y")]=[(5),(-6)]`

By R₂ – 3R₁, we get,

`[(2,1),(0,7)][("x"),("y")]=[(5),(-21)]`

∴ `[(2"x"+"y"),(0+7"y")]=[(5),(-21)]`

By equality of matrices,

2x + y = 5  ........(1)

7y = − 21  ........(2)

From (2), y = − 3

Substituting y = − 3 in (1), we get,

2x − 3 = 5

∴ 2x = 8

∴ x = 4

Hence, x = 4, y = − 3 is the required solution.