**Solve linear equations :**

Solve means we have to find the value of the variable given in the question.

Equations having variables with the highest power as '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.

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

- 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.

Let us see some example problems based on solving linear equations in one variable.

**Example 1 :**

Solve 6r + 7 = 13 + 7r

**Solution :**

6r + 7 = 13 + 7r

Subtract 7r on both sides

6r - 7r + 7 = 13 - 7r

-1r + 7 = 13

Subtract 7 on both sides

-1r + 7 - 7 = 13 - 7 ==> -r = 6 ==> r = - 6

Hence the value of r is -6.

**Example 2 :**

Solve 13 - 4x = 1 - x

**Solution :**

13 - 4x = 1 - x

Add x on both sides

13 - 4x + x = 1 - x + x

13 - 3x = 1

Subtract 13 on both sides

13 - 13 - 3x = 1 - 13

-3x = -12

Divide by -3 on both sides

x = 4

Hence the value of x is 4.

**Example 3 :**

Solve −7x − 3x + 2 = −8x − 8

**Solution :**

−7x − 3x + 2 = −8x − 8

First we have to combine the x terms in the left hand side.

−10x + 2 = −8x − 8

Now add 8x on both sides

-10x + 8x + 2 = -8x + 8x - 8

-2x + 2 = -8

Subtract 2 on both sides

-2x + 2 - 2 = -8 - 2

-2x = -10

Divide by -2 on both sides

x = 5

Hence the value of x is 5.

**Example 4 :**

Solve −7x − 3x + 2 = −8x − 8

**Solution :**

−7x − 3x + 2 = −8x − 8

First we have to combine the x terms in the left hand side.

−10x + 2 = −8x − 8

Now add 8x on both sides

-10x + 8x + 2 = -8x + 8x - 8

-2x + 2 = -8

Subtract 2 on both sides

-2x + 2 - 2 = -8 - 2

-2x = -10

Divide by -2 on both sides

x = 5

Hence the value of x is 5.

**Example 5 :**

Solve −14 + 6b + 7 − 2b = 1 + 5b

**Solution :**

−14 + 6b + 7 − 2b = 1 + 5b

First we have to combine b terms and constants in the left hand side.

−7 + 4b = 1 + 5b

Subtract by 5b on both sides

-7 + 4b - 5b = 1 + 5b - 5b

-b - 7 = 1

Subtract 7 on both sides

-b - 7 + 7 = 1 + 7

-b = 8 ==> b = -8

Hence the value of b is -8.

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

After having gone through the stuff given above, we hope that the students would have understood "Solve linear-equations".

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