Breath Math

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).

Solution:

Let the cost of the notebook be ‘x’ and the cost of the pen be ‘y’

Then by the given data, x = 2y

This can be written as x – 2y = 0

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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 = 9.3

Solution:

2x + 3y – 9.3 = 0

Therefore, a = 2 , b = 3 , c = – 35

 

(ii) x – ^y/₅ – 10 = 0

Solution:

a = x ; b = – ¹/₅ ; c = -10

 

(iii) –2x + 3y = 6

-2x + 3y – 6 = 0

a = -2 ; b = 3 ; c = -6

 

(iv) x = 3y

x – 3y = 0

Thus, a = 1 ; b = -3 ; c = 0

 

(v) 2x = –5y

2x + 5y = 0

a = 2 and b = 5 , c = 0

 

(vi) 3x + 2 = 0

3x + 0.y + 2 = 0

a = 3 ; b = 0 ; c = 2

 

(vii) y – 2 = 0

0.x + y – 2 = 0

a = 0 ; b = 1 and c = -2

 

(viii) 5 = 2x

– 2x + 5 = 0

– 2x + 0.y + 5 = 0

Thus, a = -2 ; b = 0 and c = 5

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