These NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.1 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Exercise 4.1

Question 1.

The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

Solution:

Let the cost of a notebook is Rs. x and the cost of a pen is Rs. y

According to question

x = 2y or, x – 2y = 0

Therefore the linear equation in two variables to represent this statement is x – 2y = 0

Question 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.\(\bar{35}\)

(ii) x – \(\frac {y}{5}\) – 10 = 0

(iii) -2x + 3y = 6

(iv) x = 3y

(v) -2x = -5y

(vi) 3x + 2 = 0

(vii) y – 2 = 0

(viii) 5 = 2x

Solution:

(i) We have given that

2x + 3y = 9.\(\bar{35}\)

2x + 3y – 9.\(\bar{35}\) = 0

Now, it is the form of ax + by + c = 0

Therefore the values of a, b and c are 2, 3 and -9.\(\bar{35}\) respectively.

(ii) We have given that

x – \(\frac {y}{5}\) – 10 = 0

We can also write

1x + (\(\frac {-y}{5}\)) y + (-10) = 0

Now, it is in the form of ax + by + c = 0

Therefore values of a, b and c are 1, \(\frac {-y}{5}\), and -10 respectively.

(iii) We have given that

-2x + 3y = 6

or, -2x + 3y – 6 = 0

We can also write

(-2)x + 3y + (-6) = 0

Now, it is in the form of ax + by + c = 0

Therefore, the values of a, b and c are -2, 3 and -6 respectively.

(iv) We have given that,

x = 3y

or, x – 3y = 0

We can also write

1x + (-3)y + 0 = 0

Now, it is in the form of ax + by + c = 0 and the values of a, b and c are 1, -3 and 0 respectively.

(v) We have given that

2x = -5y

or, 2x + 5y = 0

We can also write 2x + 5y + 0 = 0

Now, it is in the form of ax + by + c = 0.

Therefore, the values of a, b and c are 2, 5 and 0 respectively.

(vi) We have given that

3x + 2 = 0

We can also write 3x + 0y + 2 = 0

Now, it is in the form of ax + by + c = 0

Therefore, the values of a, b and c are 3, 0 and 2 respectively.

(vii) y – 2 = 0

We can also write,

0x + 1y + (-2) = 0

Now, it is in the form of ax + by + c = 0.

Therefore, the values of a, b and c are 0, 1 and -2 respectively.

(viii) we have given that

5 = 2x

or, 2x – 5 = 0

We can also write

2x + 0y + (-5) = 0

Now it is in the form of ax + by + c = 0.

Therefore, the values of a, b and c are 2, 0 and (-5) respectively.