Thursday, July 29, 2010

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.
(Take the cost of a notebook to be Rs x and that of a pen to be Rs y.)

Ans.
Let the cost of a notebook and a pen be x and y respectively.
Cost of notebook = 2 × Cost of pen
x = 2y
x − 2y = 0

Question 2:
Express the following linear equations in the form ax + by + c = 0 and indicate the values of ab, c in each case:
(i)  (ii)  (iii) − 2x + 3 y = 6
(iv) x = 3y (v) 2x = − 5y (vi) 3x + 2 = 0
(vii) y − 2 = 0 (viii) 5 = 2x

Ans.
(i)
= 0
Comparing this equation with ax + by = 0,
= 2, = 3, 
(ii)
Comparing this equation with ax + by c = 0,
= 1, =, c = −10
(iii) − 2x + 3 y = 6
− 2x + 3 y − 6 = 0
Comparing this equation with ax + by c = 0,
= −2, b = 3, c = −6
(iv) x = 3y
1x − 3y + 0 = 0
Comparing this equation with ax + by c = 0,
= 1, b = −3, c = 0
(v) 2x = −5y
2x + 5y + 0 = 0
Comparing this equation with ax + by c = 0,
= 2, b = 5, c = 0
(vi) 3x + 2 = 0
3x + 0.y + 2 = 0
Comparing this equation with ax + by c = 0,
= 3, b = 0, c = 2
(vii) y − 2 = 0
0.x + 1.y − 2 = 0
Comparing this equation with ax + by c = 0,
= 0, = 1, c = −2
(vii) 5 = 2x
− 2x + 0.y + 5 = 0
Comparing this equation with ax + by c = 0,
= −2, = 0, c = 5