# SOLVE LINEAR EQUATIONS

Solve Linear Equations :

In math, the word "Solve" means, we have to find the value of the variable given in the question.

Equations having variables with the highest power 1 are called linear equations.

For example 2x + 3 = 5 is known as linear equation in one variable.

2x + 3y = 5 is known as linear equation in two variables.

Here, we are going to see how to solve linear equations in one variable and two variables.

## How to solve linear equations in one variable ?

To solve linear equations in one variable, we have to follow the steps given below.

• Bring the variables to one side of the equation. Usually we prefer left hand side.
• Bring the values to the another side of the equation. Usually we prefer right hand side.
• In order to move variables and values from one side to another side we use inverse operations for this purpose.

## Solving Linear Equations with One Variable - Examples

Example 1 :

Solve for r :

6r + 7  =  13 + 7r

Solution :

6r + 7 = 13 + 7r

Subtract 7r and 7 from each side.

- r  =  6

Multiply each side (-1).

r  =  - 6

So, the the value of r is -6.

Example 2 :

Solve for x :

13 - 4x  =  1 - x

Solution :

13 - 4x  =  1 - x

13 - 3x  =  1

Subtract 13 from each side.

- 3x  =  - 12

Divide each side by (-3)

x  =  4

So, the value of x is 4.

Example 3 :

Solve for x :

- 7x - 3x + 2  =  - 8x - 8

Solution :

- 7x - 3x + 2  =  - 8x - 8

Combine the like term.

- 10x + 2  =  - 8x - 8

- 2x + 2  =  - 8

Subtract 2 from each side.

- 2x  =  - 10

Divide each side by (-2).

x  =  5.

So, the value of x is 5.

Example 5 :

Solve for b :

- 14 + 6b + 7 - 2b  =  1 + 5b

Solution :

- 14 + 6b + 7 - 2b  =  1 + 5b

Combine the like term.

4b - 7  =  1 + 5b

Subtract 5b from each side.

- b - 7  =  1

- b  =  8

Multiply each side by (-1).

b  =  - 8

So, the value of b is -8.

## How to solve linear-equations in two variables ?

We can follow the below methods to solve linear equations in two variables.

To know each of the methods given below in detail, please click on the links. After having gone through the stuff given above, we hope that the students would have understood, how to solve linear equations.

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