Students can go through AP 8th Class Maths Notes Chapter 2 Linear Equations in One Variable to understand and remember the concepts easily.
Class 8 Maths Chapter 2 Notes Linear Equations in One Variable
→ An algebraic equation is an equality involving variables. It says that the value of the
expression on one side of the equality sign is equal to the value of the expression on the other side.
→ The expressions which form the equation contain only one variable. Further, the equations are linear, i.e., the highest power of the variable appearing in the equation is 1.
→ A linear equatiop may have for its solution any rational number.
→ An equation may have linear expressions on both sides.
→ Just as numbers, variables can, also, be transposed from one side of the equation to the other.
→ Occasionally, the expressions forming equations have to be simplified before we can solve them by usual methods. Some equations may not even be linear to begin with, but they can be brought to a linear form by multiplying both sides of the equation by a suitable expression.
→ The utility of linear equations is in their diverse applications; different problems on numbers, ages, perimeters, combination of currency notes, and so on can be solved using linear equations.
→ Variables : x, y , z, …………, p, q, r, …………..
→ Constants : 1, 2, 3, ………… , -10,-11,-12, …………… etc.
→ Co-efficient: Example 5
→ Expression : Combination of one or more terms with some variables, constants etc.
Ex : 2x, 3xy2 + 10, 2xy + yz + zx2 + ………
| Expression | No.of variables | Highest power | Name of expression |
| 1) 2x + 3 | 1(x) | 1 | Linear expression with one variable (x) |
| 2) 3x2 + 4x + 10 | 1(x) | 2(in 3x2) | Quadratic expression with one variable (x) |
| 3) 2x – 3y + 4 | 2(x, y) | 1 | Linear equation with two variables (x, y) |
| 4) 3x + 4y – 6z – 10 | 3 (x, y, z) | 1 | Linear equation with three variables (x, y, z) |
→ Equation : Two expressions linked with the relation of equality is called equation.
Equation format: Expression (1) = Expression (2)
LHS = RHS
‘=’ symbol is present i : equation.
Whereas in an expression there wont be the symbol ‘=’.
Examples:
| Equation | LHS | RHS | Order (or) highest power | Variables | Name of the equation |
| a) 2x + 5 = 10 | 2x + 5 | 10 | 1 | x | Linear equation in one variable |
| b) 2x + 3y = 4x – 10 | 2x + 3y | 4x – 10 | 1 | x, y | Linear equation in two variables |
| c) ax2 + bx + c = 0 | ax2 + bx + c | 0 | 2 | x | Quadratic equation in one variable |
Definition (2) : An algebraic equation is an equality involving variabies. It should have an equality sign.
i) The expression on the left side of the equality sign is called LHS.
ii) The expression on the right of the equality sign is called RHS.
Solution : For what value of variable the equality of LHS and RHS happens true, that value is called solution of the equation.
For example, check which of the values 1,2,3,4 is solution of equation 3x – 5 = 4. Let us check for x = 1 [here variable of given equation 3x – 5 = 4 is x]
So, 3x – 5 = 4
for x = 1 ⇒ 3(1) -5 = 4
⇒ 3 – 5 = 4
⇒ -2 = 4 this is false.
So, x = 1 is not the solution of given equation.
Checking x = 2
Substitute x = 2 in given equation 3x – 5 = 4
We get 3(2)-5 = 4
⇒ 6 – 5 = 4
⇒ 1 = 4 this is false.
So x = 2 is not a solution.
Now, checking x = 3
Putting x = 3 in given equation 3x – 5 = 4
⇒ 3(3) – 5 = 4
⇒ 9 – 5 = 4
⇒ 4 = 4
∴ LHS = RHS this is true.
Hence x =3 is a solution to given equation.
Now checking x = 4
Put x = 4 in 3x – 5 = 4
⇒ 3(4) – 5 = 4
⇒ 12 – 5 = 4
⇒ 7 = 4
This is false. So x = 4 is not a solution.
→ Steps to find the solution of linear equation :
- Identify the variables on both sides.
- Identify the constants on both sides.
- Shift all variables to one side and the remaining constants to other side. (by additive / multiplicative inverses or transpose method)
- Get solution.