Linear Equations (I)

Linear Equations In One Unknown

1. A linear term is a term with one unknow and the power of the unknown is one.Example: 5m, 10n, ½p → Linear terms8x², 3ab, 6y ³z → Non-linear terms

2. A linear algebraic expression is formed when two or more terms with the power of one are combined by addition or subtraction or both.

Example:

3x-4y → linear expression

4m+5n → linear expression

a²+3 → not a linear expression

3. A linear equation involves only expressions where the power of the unknowns is one

Example:

4m + 7n = 10 → linear equation

9a² + 3 = 8 → not a linear equation

4. A linear equation in one unknown is an equation which shows the relationship between numbers and a linear term with one unknown.

Example:

2k + 3 = 6 → linear equation in one unknown

4x + 5y = 8 → not a linear equation in one because it consists of two unknowns, x and y.

Solutions of Linear Equations in One Unknown

1. Solving linear equation is a process of finding the value of an unknown which satisfies the equation.

2. the solutions of the equations are also known as the roots of the equations.

3. A linear equation in one unknown has only one root.

4. We can determining the solution of a linear equation by trial and improvement method, but not all the equations can be easily solved by this method.

5. There are 4 methods to solve linear equations in one unknown, depending on the form of the equations.
Example:
(i) Using subtraction (ii) Using addition
x + 8 = 14 
x + 8 -8 = 14 - 8 
x = 6 

(ii) Using addition
x - 3 = 7
x - 3 + 3 = 7 + 3
x = 10

(iii) Using division (iv) Using multiplication
5x = 15 x/5 = 6
5x ÷ 5 = 15 ÷ 5 x/5 x 5 = 6 x 5
x = 3 x = 30

(iv) Using multiplication
x/5 = 6
x/5 x 5 = 6 x 5
x = 30