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Exercise - 4.1

Linear Equations in Two Variables

**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).

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 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

(i) 2x + 3y = 9.35 2x + 3y - 9.35 = 0 Compairing the equation with equation ax + by + c = 0 a = 2, b = 3, c = - 9.35 (ii) x- y/5 - 10 = 0 5x - y - 50 = 0 Compairing the equation with equation ax + by + c = 0 a = 5, b = -1, c = -50 (iii) –2x + 3y = 6 -2x + 3y - 6 = 0 Compairing the equation with equation ax + by + c = 0 a = -2, b = 3, c = -6 (iv) x = 3y x - 3y = 0 Compairing the equation with equation ax + by + c = 0 a = 1, b = -3, c = 0 (v) 2x = –5y 2x + 5y = 0 Compairing the equation with equation ax + by + c = 0 a = 2, b = 5 c = 0 (vi) 3x + 2 = 0 Compairing the equation with equation ax + by + c = 0 a = 3, b = 0, c = 2 (vii) y – 2 = 0 Compairing the equation with equation ax + by + c = 0 a = 0, b = 1, c = -2 (viii) 5 = 2x 2x - 5 = 0 Compairing the equation with equation ax + by + c = 0 a = 2, b = 0, c = -5

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