Solution of a Linear Equation – Transpose Method

# Solution of a Linear Equation – Transpose Method

Fill Out the Form for Expert Academic Guidance!

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

• Transpose of a Term
• Solving Equation by Transpose Method
• Summary
• What’s Next?

In the previous segment of Class 6 Maths, we learnt how to solve a linear equation by inverse method. In this segment, we will learn how to solve a linear equation by the transpose method.

## What is Transpose of a term?

Transpose of a term means transferring the term from its place to the opposite side in an equation. The following transpositions keep the overall value of the equation unchanged:

• If a term is added on one side of an equation, then it is subtracted when transposed to the other side.

For example, 10x + 3 = 43.

Here, 3 can be transposed from L.H.S. to the R.H.S. as follows: 10x = 43 – 3

• If a term is subtracted on one side of an equation, then it is added when transposed to the other side.

For example, y – 10 = 4.

Here, 10 can be transposed from L.H.S. to the R.H.S. as follows: y = 4 + 10

• If a term is multiplied on one side of an equation, then it is divided when transposed to the other side.

For example, 16z = 32.

Here, 16 can be transposed from L.H.S. to the R.H.S. as follows:

z = 32

16

• If a term is divided on one side of an equation, then it is multiplied when transposed to

the other side.

For example, 3? = 4.

2

Here, 2 can be transposed from L.H.S. to the R.H.S. as follows:

3p = 4 x 2

## How to find the Solution of an equation by transpose method

Let us understand how to find the solution of a linear equation in one variable by the inverse method for 15y – 2 = 12y + 4, using the following steps:

Step 1: Identify the constant terms and the variables in the L.H.S. and the R.H.S. of the equation.

Here, the constant term in L.H.S. is 2 and that in the R.H.S. is 4. The variable in L.H.S. is 15y and that in R.H.S. is 12y.

Step 2: Collect all constants to one side of the equation and the variables to the other side with the help of transposition.

Here, 2 will be transposed from L.H.S. to R.H.S. Since 2 is subtracted in the L.H.S., it will be added in the R.H.S.

Similarly, 12y will be transposed from R.H.S. to L.H.S. Since 12y is added in the L.H.S., it will be subtracted in the R.H.S.

That is, 15y – 12y = 4 + 2

∴ 3y = 6

Step 3: Transpose the coefficient of the variable from one side to the other side.

So, y = 6

3

∴ y = 2

## Summary

Transpose of a Term

Transferring the term from its place to the opposite side in an equation

What’s next?

In our next segment of Class 6 Maths, we will understand how to solve an equation using the flowchart method.