Chapter 4. Linear Equation In Two Variables
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 'x' and that of a pen to be 'y' )
Solution:
Let the cost of pen = y
Let the cost of notebook= x
Then, According To Question,
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
Solution:
(i) 2x + 3y = 9.35
Expressing the equation in the form of ax + by + c = 0,
∴ 2x+3y-9.35= 0
On Comparing, We have
Then, a= 2, b= 3, c= -9.3
(ii) x – 5y – 10 = 0
Solution:
(ii) x – 5y – 10 = 0
Expressing the equation in the form of ax + by + c = 0,
∴ x- 5y - 10 = 0
On Comparing, We have
Then, a= 1, b= -5, c= -10
(iii) –2x + 3y = 6
Solution:
(iii) –2x + 3y = 6
Expressing the equation in the form of ax + by + c = 0,
∴ -2x + 3y - 6= 0
On Comparing, We have
Then, a= -2, b= 3, c= -6
(iv) x = 3y
Solution:
(iv) x = 3y
Expressing the equation in the form of ax + by + c = 0,
∴ x - 3y= 0
On Comparing, We have
Then, a= 1, b= -3, c= 0
(v) 2x = –5y
Solution:
(v) 2x = –5y
Expressing the equation in the form of ax + by + c = 0,
∴ 2x + 5y= 0
On Comparing, We have
Then, a= 2, b= 5, c= 0
(vi) 3x + 2 = 0
Solution:
(vi) 3x + 2 = 0
Expressing the equation in the form of ax + by + c = 0,
∴ 3x + 2= 0
On Comparing, We have
Then, a= 3, b= 0, c= 2
(vii) y – 2 = 0
Solution:
(vii) y – 2 = 0
Expressing the equation in the form of ax + by + c = 0,
∴ y-2= 0
On Comparing, We have
Then, a= 0, b= 1, c= -2
(viii) 5 = 2x
Solution:
(viii) 5 = 2x
Expressing the equation in the form of ax + by + c = 0,
∴ 2x - 5= 0
On Comparing, We have
Then, a= 2, b= 0, c= -5
