# Linear Equations

## 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 the above statement.

Answer: Let the cost of a notebook be x and that of a pen be y.
According to question,
The cost of a notebook is twice the cost of a pen
Or, x = 2y
Or, 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 = 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

Solution: (i) a = 2, b = 3 and c = 9.35

(ii) a = 1, b = (-1/5) and c = -10

(iii) -2x + 3y = 6
Or, -2x + 3y – 6 = 0
Comparing the equation with ax + by + c = 0, we have
a = -2, b = 3, c = -6

(iv) x = 3y
Or, x - 3y = 0
Comparing the equation with ax + by + c = 0, we have
a = 1, b = -3, c = 0

(v) 2x = -5y
Or, 2 x + 5y = 0
Comparing the equation with ax + by + c = 0, we have
a = 2, b = 5, c = 0

(vi) 3x + 2 = 0
3 x + 0y + 2 = 0
Comparing the equation with ax + by + c = 0, we have
a = 3, b = 0, c = 2

(vii) y – 2 = 0
Or, 0 x + 1y - 2 = 0
Comparing the equation with ax + by + c = 0, we have
a = 0, b = 1, c = -2

(viii) 5 = 2x
Or, -2x - 0y + 5 = 0
Comparing the equation with ax + by + c = 0, we have
a = -2, b = 0, c = 5