    # 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.

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.

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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