The document Ex 4.1 NCERT Solutions - Linear Equations in Two Variables Class 9 Notes | EduRev is a part of the Class 9 Course Class 9 Mathematics by Full Circle.

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**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. (Take the cost of a notebook to be ₹ x and that of a pen to be ₹ y).Solution:** Let the cost of a notebook =

The cost of a pen =

According to the condition,

we have [Cost of a notebook] = 2 x [Cost of a pen]

i.e. [x] = 2 x [y]

or

x = 2y

or

x – 2y = 0

Thus, the required linear equation 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 = ****(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****Solution:** (i) We have 2x + 3y =

∴ (2)x + (3)y + (–) = 0

Comparing it with ax + bx + c = 0,

we have a = 2, b = 3 and c = –.

(ii) We have x –(y/5) – 10 = 0

or

Comparing with ax + bx + c = 0, we get

**Note:** Above equation can also be compared by:

Multiplying throughout by 5,

or 5x – y – 50 = 0

or 5(x) + (–1)y + (–50) = 0

Comparing with ax + by + c = 0,

we get a = 5, b = –1 and c = –50.

(iii) We have –2x + 3y = 6

⇒ –2x + 3y – 6 = 0

⇒ (–2)x + (3)y + (–6) = 0

Comparing with ax + bx + c = 0,

we get a = –2, b = 3 and c = –6.

(iv) We have x = 3y

⇒ x – 3y = 0

⇒ (1)x + (–3)y + 0 = 0

Comparing with ax + bx + c = 0,

we get a = 1, b = –3 and c = 0.

(v) We have 2x = –5y

⇒ 2x + 5y = 0

⇒ (2)x + (5)y + 0 = 0

Comparing with ax + by + c = 0,

we get a = 2, b = 5 and c = 0.

(vi) We have 3x + 2 = 0

⇒ 3x + 2 + 0y = 0

⇒ (3)x + (0)y + (2) = 0

Comparing with ax + by + c = 0,

we get a = 3, b = 0 and c = 2.

(vii) We have y – 2 = 0

⇒ (0)x + (1)y + (–2) = 0

Comparing with ax + by + c = 0,

we have a = 0, b = 1 and c = –2.

(viii) We have 5 = 2x

⇒ 5 – 2x = 0

⇒ –2x + 0y + 5 = 0

⇒ (–2)x + (0)y + (5) = 0

Comparing with ax + by + c = 0,

we get a = –2, b = 0 and c = 5.

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