R.D. Sharma Solutions Class 9th: Ch 13 Linear Equations in Two Variables Exercise 13.1

Chapter 13 Linear Equations in Two Variables R.D. Sharma Solutions for Class 9th Exercise 13.1

Exercise 13.1

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
(v) 2x+ 3 = 0
(vi) y - 5 = 0
(vii) 4 = 3x
(viii) y = x/2

Solution

(i) We are given
-2x + 3y = 12
-2x + 3y – 12 = 0
Comparing the given equation with ax+ by+ c = 0
We get, a = – 2; b = 3; c = -12

(ii) We are given
x – y/2 – 5= 0
Comparing the given equation with ax + by + c = 0 ,
We get, a = 1; b = -1/2, c = -5

(iii) We are given
2x + 3y = 9.35
2x + 3y – 9.35 =0
Comparing the given equation with ax + by + c = 0
We get, a = 2 ; b = 3 ; c = -9.35

(iv) We are given
3x = -7y
3x + 7y = 0
Comparing the given equation with ax+ by + c = 0,
We get, a = 3 ; b = 7 ; c = 0

(v) We are given
2x + 3 = 0
Comparing the given equation with ax + by + c = 0,
We get, a = 2 ; b = 0 ; c = 3

(vi) We are given Y – 5 = 0
Comparing the given equation with ax + by+ c = 0,
We get, a = 0; b = 1; c = -5

(vii) We are given
4 = 3x
3x-4 = 0
Comparing the given equation with ax + by + c = 0,
We get, a = 3; b = 0; c = -4

 (viii) We are given
Y = x/2
Taking L.C.M => x — 2y = 0
Comparing the given equation with ax + by + c = 0 ,
We get, a = 1; b = -2; 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 = 3/2 x

Solution

(i) We are given,
2x = -3
Now, in two variable forms the given equation will be
2x + 0y + 3=0

(ii) We are given,
y = 3
Now, in two variable forms the given equation will be
 0 x + y – 3 = 0

(iii) We are given,
5x = -7/2
Now, in two variable forms the given equation will be
5x + 0y +7/2 = 0
10x + 0y – 7 = 0

(iv) We are given,
y = 3/2 x
Now, in two variable forms the given equation will be
3/2 x - y + 0 = 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 the cost of fountain pen be y and cost of ball pen be x.
According to the given equation, we have
x = y/2 - 5
⇒ 2x = y - 10
⇒ 2x - y + 10 = 0

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