NCERT Solutions Class 9 Mathematics

Exercise 4.1

Q.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 x and that of a pen to be y).

Q.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:

NCERT Solutions Class 9 Mathematics

Exercise 4.1

Q.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 x and that of a pen to be y).

Solution:

Let the cost of notebook be x and the cost of pen be y.

Then, ATQ,

Cost of a notebook = twice the cost of pen

⇒ x = 2y

⇒ x - 2y = 0

Q.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 - $\frac{\mathrm{y}}{5}$ - 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) 2x + 3y = 9.35

⇒ 2x + 3y - 9.35 = 0

Comparing this equation with ax + by + c = 0, we get, a = 2, b = 3 and c = -9.35

(ii) x - $\frac{\mathrm{y}}{5}$ - 10 = 0

Comparing this equation with ax + by + c = 0, we get, a = 1, b = - and c = -10

(iii) -2x + 3y = 6

⇒ -2x + 3y - 6 = 0

Comparing this equation with ax + by + c = 0, we get, a = -2, b = 3 and c = -6

(iv) x = 3y

⇒ x - 3y = 0

Comparing this equation with ax + by + c = 0, we get, a = 1, b = -3 and c = 0

(v) 2x = -5y

⇒ 2x + 5y = 0

Comparing this equation with ax + by + c = 0, we get, a = 2, b = 5 and c = 0

(vi) 3x + 2 = 0

⇒ 3x + 0y + 2 = 0

Comparing this equation with ax + by + c = 0, we get, a = 3, b = 0 and c = 2

(vii) y - 2 = 0

⇒ 0x + y - 2 = 0

Comparing this equation with ax + by + c = 0, we get, a = 0, b = 1 and c = -2

(viii) 5 = 2x

⇒ 2x + 0y - 5 = 0

Comparing this equation with ax + by + c = 0, we get,a = 2, b = 0 and c = -5