# SOLVE LINEAR EQUATIONS

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

To solve a linear equation in one variable, we have to isolate the variable we have in the equation.

To isolate the variable, we have to get rid of all the values around the variable in the equation.

Consider the following linear equation in one variable.

2x + 3 = 13

To solve for x in the above equation, we have to get rid of the values 2 and 3 around the variable x using properties of equality.

In the equation above, to get rid of +3, we have to subtract 3 from both sides.

(2x + 3) - 3 = 13 - 3

2x + 3 - 3 = 10

2x = 10

In 2x = 10, to get rid of the '2' which is multiplied by x. divide both sides of the equation by 2.

2x/2 = 10/2

x = 5

The value of x in the given is 5.

## Solving Linear Equations in One Variable

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.

## Solving 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.

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