Chapter 13 Linear Equations in Two Variables RD Sharma Solutions Exercise 13.1 Class 9 Maths
Chapter Name  RD Sharma Chapter 13 Linear Equations in Two Variables Exercise 13.1 
Book Name  RD Sharma Mathematics for Class 10 
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Related Study  NCERT Solutions for Class 10 Maths 
Exercise 13.1 Solutions
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  y/2  5 = 0
(iii) 2x + 3y = 9.35
(iv) 3x = 7y
Solution
(i) We have
2x + 3y = 12
⇒ 2x + 3y  12 = 0
On comparing this equation with ax + by + c = 0 we obtain a = 2, b = 3 and c = 12.
(ii) Given that
x  y/2  5 = 0
1x  y/2  5 = 0
On comparing this equation with ax + by + c = 0 we obtain a = 1, b = 1/2 and c = 5
(iii) Given that
2x + 3y = 9.35
⇒ 2x + 3y  9.35 = 0
On comparing this equation with ax + by +c = 0 we get a = 2, b = 3 and c = 9.35
(iv) 3x = 7y ⇒ 3x + 7y + 0 = 0
On comparing this equation with ax + by + c = 0 we get a = 3, b = 0 and c = 3
(v) We have
2x + 3 = 0
2x + 0(y) + 3 = 0
On comparing this equation with ax + by + c = 0 we get a = 2, b = 0 and c = 3
(vi) Given that
y  5 = 0
⇒ 0x + 1y  5 = 0
On comparing this equation with ax + by + c = 0 we get a = 0, b = 1 and c = 5
(vii) We have
4 = x
3x + 0.y + 4 = 0
On comparing the equation with ax + by + c = 0 we get a = 3, b = 0 and c = 4
(viii) Given that,
y = x/2
⇒ 2y = x
⇒ x  2y + 0 = 0
On comparing this equation with ax + by + c = 0 we get a = 1, b = 2 and c = 0
2. Write each of the following as an equation in two variables:
(i) 2x =  3
(ii) y = 3
(iii) 5x = 7/2
(iv) y = 3x/2
Solution
(i) We have
2x =  3
⇒ 2x + 3 = 0
⇒ 2x + 0.y + 3 = 0
(ii) We have,
y = 3
y  3 = 0
⇒ 0.x + 1.y  3 = 0
(iii) Given
5x = 7/2
10x  7 = 0
10x + 0.y  7 = 0
(iv) We have
y = 3x/2
3x  2y = 0
3x  2y + 0 = 0
3. The cost of ball pen is Rs. 5 less than half of the cost of fountain pen. Write this statement as a linear equation in two variables.
Solution
Let us assume the cost of the ball pen be Rs. x and that of a fountain pen to be y then according to given statements
We have
x = y/2  5
⇒ 2x = y  10
⇒ 2x  y + 10 = 0