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RD Chapter 7 Introduction to Euclid s Geometry Ex 7.1 Solutions

Question - 1 : - 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 = 12
(ii) x-  -5 = 0
(iii) 2x + 3y = 9.35
(iv) 3x = -7y
(v) 2x + 3 = 0
(vi) y – 5 = 0
(vii) 4 = 3x
(viii) y =  

Answer - 1 : -

(i) -2x + 3y = 12
⇒  -2x + 3y – 12 = 0
Here a -2, b = 3, c = – 12
(ii) x –   -5 = 0
Here a = 1, b =  ,c = -5
(iii) 2x + 3y = 9.35
⇒  2x + 3y – 9.35 = 0
Here a = 2, b = 3, c = – 9.35
(iv) 3x = -7y
⇒  3x + 7y + 0 = 0
Here a = 3, b = 7,c = 0
(v) 2x + 3 = 0
⇒ 2x + 0y + 3 = 0
Here a = 2, b = 0, c = 3
(vi) y-5 = 0 ⇒ ox+y-5 = 0
Here a = 0, b = 1, c = -5
(vii) 4 = 3x
⇒ 3x – 4 = 0
⇒ 3x + 0y – 4 = 0
Here a = 3, b = 0, c = -4
(Viii) y=  
 ⇒   – y+ 0 = 0
⇒  x-2y + 0 = 0
Here a = 1, y = -2, c = 0

Question - 2 : -
Write each of the following as an equation in two variables.
(i) 2x = -3
(ii) y = 3
(iii) 5x =  
(iv) y = x

Answer - 2 : -

(i) 2x = -3⇒  2x + 3 = 0
⇒ 2x + 0y + 3 = 0
(ii) y= 3 ⇒  y-3=0
⇒  0x+ y-3 = 0
(iii) 5x =  ⇒ 10x = 7
⇒  10x + 0y – 7 = 0
(iv) y= x⇒2y = 3x
⇒ 3x – 2y + 0 = 0

Question - 3 : - The cost of ball pen is ₹5 less than half of the cost of fountain pen. Write this statement as a linear equation in two variables.

Answer - 3 : -

Let cost of a fountain pen = ₹x
and cost of ball pen = ₹y
∴ According to the condition,
y =-5
⇒  2y = x – 10
⇒  x – 2y – 10 = 0

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