# Class 9 Maths Chapter 4 NCERT Solutions | Linear Equations In Two Variables

Chapter 4: Linear Equations in Two Variables

Summary:

1. An equation of the form ax+by+c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in two variables.

2. A linear equation in two variables has infinitely many solutions.

3. The graph of every linear equation in two variables is a straight line.

4. x = 0 is the equation of the y – axis and y = 0 is the equation of the x – axis.

5. The graph of x = a is a straight line parallel to the y – axis.

6. The graph of y = a is a straight line parallel to the x – axis.

7. An equation of the type y = mx represents a line passing through the origin.

### Exercise 4.1

1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
(Take the cost of a notebook to be Rs x and that of a pen to be Rs y)

Let the cost of a notebook be x.
Let the cost of a pen be y.
Given that the cost of a notebook is twice the cost of a pen.
Therefore, we can write the linear equation as x = 2y
x -2y = 0

2. Express the following linear equations in the form ax + by + c =0 and indicate the values of a, b and c in each case:

i) 2x + 3y = 9.35
ii) x – y/5 – 10 = 0
iii) -2x + 3y = 6
iv) x = 3y
v) 2x = -5y
vi) 3x + 2 = 0
vii) y – 2 = 0
viii) 5 = 2x

i) 2x +3y = 9.35 can be written as 2x + 3y – 9.35 = 0.
Here a = 2, b = 3 and c= -9.35
ii) x – y/5 – 10 = 0 is of the form ax + by + c = 0, where a = 1, b= -1/5 and c= -10.
iii) -2x + 3y = 6 can be written as -2x + 3y – 6 = 0.
Here a = -2, b = 3 and c = -6
iv) x = 3y can be written as 1x – 3y+0 = 0.
Here a = 1, b= -3 and c=0
v) 2x = -5y can be written as 2x + 5y + 0 = 0
Here a = 2, b=5 and c=0
vi) 3x + 2 = 0 can be written as 3x + 0y + 2 = 0
Here a = 3, b = 0 and c=2
vii) y – 2 = 0 can be written as 0.x + 1.y – 2 = 0
Here a = 0, b= 1 and c= -2
viii) 5 = 2x can be written as -2x + 0.y + 5 = 0
Here a = -2, b= 0 and c = 5