# Linear Equation

__LINEAR EQUATION IN ONE VARIABLE:__
A linear equation in one variable is represented as ax + b = 0, where a ≠ 0.

2x + 1 = 0, √3y + √2 = 0 are examples of linear equations in one variable.

2x + 1 = 0, √3y + √2 = 0 are examples of linear equations in one variable.

A linear equation has one and only one solution which can be represented on a number
line. For example, the solution of the linear equation 2x + 3 = 0 is x = -3/2 i.e.
-1.5 which can be represented on the number line as given below:

__LINEAR EQUATION IN TWO VARIABLE:__
A linear equation in two variables is of the form ax + by + c = 0, where a, b and
c are real numbers and a, b ≠ 0.

For example: 2x + 3y = 7, p + 6q = 5 are linear equations in two variables.

For example: 2x + 3y = 7, p + 6q = 5 are linear equations in two variables.

*Example 1:*
Write equations

**a)**2x + 3y = 4.37 and**b)**x – 4 = √3y in the form ax + by + c = 0 and indicate the values of a, b and c in each.

*Solution:***a)**2x + 3y = 4.37 => 2x + 3y – 4.37 = 0

Comparing with ax + by + c = 0, we get

a = 2, b = 3 and c = -4.37

**(Answer)**

**b)**x – 4 = √3y => x - √3y – 4 = 0

Comparing with ax + by + c = 0, we get

a = 1, b = - √3 and c = -4

**(Answer)**

*Example 2:*
Write the following as an equation in two variables:

**a)**y = 3 and**b)**2x = 5.

*Solution:***a)**y = 3 => y – 3 = 0 => 0.x + 1.y - 3 = 0 => 0x + 1y - 3 = 0

**(Answer)**

**b)**2x = 5 => 2x – 5 = 0 => 2.x + 0.y – 5 = 0 => 2x + 0y -5 = 0

**(Answer)**

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