Linear Equations

An Equation having the maximum order of 1 is known as a Linear equation. It is of the form, ax + b = 0.
Example:2x – 4 = 0
2x = 4
x = 4/2 = 2

When the equation has a homogeneous variable (i.e. only one variable), then this type of equation is known as a Linear equation in one variable.


How to Solve Linear Equations:

For solving equations with variables on both sides, the following steps are followed:

Consider the equation: 5x – 9 = -3x + 19

Step 1: Transpose all the variables on one side of the equation. By transpose, we mean to shift the variables from one side of the equation to the other side of the equation. In the method of transposition, the operation on the operand gets reversed.

In the equation 5x – 9 = -3x + 19, we transpose -3x from the left-hand side to the right-hand side of the equality, the operation gets reversed upon transposition and the equation becomes:

5x – 9 +3x = 19

⇒ 8x -9 = 19

Step 2: Similarly transpose all the constant terms on the other side of the equation as below:

8x -9 = 19

⇒ 8x = 19 + 9

⇒ 8x = 28

Step 3: Divide the equation with 8 on both sides of the equality.

8x/8 = 28/8

⇒ x = 28/8

If we substitute x = 28/8 in the equation 5x – 9 = -3x + 19, we will get 9 = 9, thereby satisfying the equality and giving us the required solution.

If the equation has more than one variable then it becomes Linear equation in two variables.

Linear Equation in One variable Linear Equation in Two variable
3x+5=0

\(\frac{3}{2}x +7 = 0\)<

98x = 49

y = 7x=3

3a+2b = 5

6x+9y-12=0

The standard form of a linear equation in two variables is represented as

linear equation in one variable

Where a and b are real numbers, and both a and b are not equal to zero.

Every linear equation in one variable has a unique solution.

Both sides of the equation are supposed to be balanced for solving a linear equation. Equality sign denotes that the expressions on either side of the ‘equal to’ sign are equal. Since the equation is balanced, for solving it certain mathematical operations are performed on both sides of the equation in a manner that it does not affect the balance of the equation. For solving equations with variables on both sides, the following steps are followed:

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Practise This Question

Which of the following represents a linear equation in two variables?