CLASS 9 MATH NCERT SOLUTION FOR CHAPTER – 4 Linear Equations in Two Variables EX – 4.1

Linear Equations in Two Variables

Page No: 68

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).

Answer

Let the cost of pen be y and the cost of notebook be x.
A/q,
Cost  of a notebook = twice the pen = 2y.
∴2y = x
⇒ x – 2y = 0
This is a linear equation in two variables to represent this statement.

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

Answer

(i) 2x + 3y = 9.35
⇒ 2x + 3y – 9.35 = 0
On comparing this equation with ax + by + c = 0, we get
a = 2x, b = 3 and c = -9.35

(ii) x – y/5 – 10 = 0
On comparing this equation with ax + by + c = 0, we get
a = 1, b = -1/5 and c = -10

(iii) -2x + 3y = 6
⇒ -2x + 3y – 6 = 0
On comparing this equation with ax + by + c = 0, we get
a = -2, b = 3 and c = -6

(iv) x = 3y
⇒ x – 3y = 0
On comparing this equation with ax + by + c = 0, we get
a = 1, b = -3 and c = 0

(v) 2x = -5y
⇒ 2x + 5y = 0
On 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
On 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
On comparing this equation with ax + by + c = 0, we get
a = 0, b = 1 and c = -2

(viii) 5 = 2x
⇒ -2x + 0y + 5 = 0
On comparing this equation with ax + by + c = 0, we get
a = -2, b = 0 and c = 5

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