A linear equation is an equation whose degree is 1. i.e. In a linear equation, the highest power of the variable is 1.
Example:
i) x+3 = 5
ii) y-5=8
Solution (or) Root of a Linear Equation:
A value or a number which satisfies the given linear equation is called its root or solution.
Example:
i) 2 is the solution of x+3=5 because 2+3=5.
ii) 13 is the solution of y-5=8 because 13-5=8.
Solving a Linear Equation:
A linear equation may involve the operations addition, subtraction, multiplication or division and the following steps are to be followed for the respective operations.
i) When the variable in a linear equation is getting added to a number, the same is subtracted from the equation to obtain the solution.
Example:
x + 5 = 8
Subtracting 5 from both sides,
X = 8-5 = 3.
ii) When some number is getting subtracted from the variable in a linear equation, the same number is added to the equation to obtain the solution.
Example:
x-5 = 8
Adding 5 both sides,
x = 8+5 = 13
iii) When the variable in a linear equation is getting multiplied by a number, the equation is divided by the same number to obtain the solution.
Example:
5x = 20
Dividing both sides by 5,
x= 20/5 = 4.
iv) When the variable in a linear equation is getting divided by a number, the equation is multiplied by the same number to obtain the solution.
Example:
x/5 = 4
multiplying both sides by 5,
x = 4×5 = 20.
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