Chapter 4: Linear Equations (I)
4.1 Linear Equations In One Unknown1. A linear term is a term with one unknow and the power of the unknown is one.
Example:
5m, 10n, ½p → Linear terms
8x², 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.
4.2 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
