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

Sum

Solve the following equations by the reduction method.

2x + y = 5, 3x + 5y = – 3

#### Solution

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.

Is there an error in this question or solution?