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SAI International School
CLASS - IX

Mathematics
CHAPTER-2: Linear equation in two variable

Lesson Notes-2
Sub Topic: Solution of linear equation In Two Variables

Solution of a Linear Equation In one Variable

 There is only one solution in the linear equation in one variable
 ax + b = 0

 x= –b/a

 –b/a is the solution of the equation ax + b = 0 .

 Now consider a linear equation in two variable,ax + by + c = 0 , a≠ 0

 To find out a solution, we can put any real value of x and we will get a real value of y.
Then (x, y) is a solution of the equation ,ax + by + c = 0 , a≠ 0
Or

We have to express y in terms of x i.e, y = f(x) or We can express x in terms of y i.e, x=
f(y).

ax + by + c = 0

 by =–ax –c

 y= (–ax –c)/b

Now for every real value of x, we will get a real value of y.
 So we conclude that, there are infinitely many solutions in the linear equation in two

variables.
 As there are two variables, the solution will be in the form of an ordered pair, i.e. (x,
y).

 The pair which satisfies the equation is the solution of that particular equation.

Example:
Find the solution for the equation 2x + y = 7.

Solution:
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