SOLVE LINEAR EQUATIONS

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

Add x to each side.

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

Add 8x to each side. 

- 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

Add 7 to each side. 

- 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.

• Substitution method
• Elimination method
• Cross multiplication method
• Graphical method

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