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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