Class 9 RD Sharma Solutions – Chapter 13 Linear Equation in Two Variable – Exercise 13.1
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 – 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) -2x + 3y = 12
Rearranging,
– 2x + 3y – 12 = 0
On comparing with the given form of linear equation, ax + by + c = 0,
We get,
a = – 2
b = 3
c = -12
(ii) x – y/2 – 5 = 0
On comparing with the given form of linear equation, ax + by + c = 0,
We get,
a = 1
b = -1/2
c = -5
(iii) 2x + 3y = 9.35
Rearranging, 2x + 3y – 9.35 = 0
On comparing with the given form of linear equation, ax + by + c = 0,
We get,
a = 2
b = 3
c = -9.35
(iv) 3x = -7y
Rearranging, 3x + 7y + 0 = 0
On comparing with the given form of linear equation, ax + by + c = 0,
We get,
a = 3
b = 7
c = 0
(v) 2x + 3 = 0
Rearranging, 2x + 0y + 3 = 0
On comparing with the given form of linear equation, ax + by + c = 0,
We get,
a = 2
b = 0
c = 3
(vi) y – 5 = 0
Rearranging, 0x + y – 5 = 0
On comparing with the given form of linear equation, ax + by + c = 0,
We get,
a = 0
b = 1
c = -5
(vii) 4 = 3x
Rearranging, 3x + 0y – 4 = 0
On comparing with the given form of linear equation, ax + by + c = 0,
We get,
a = 3
b = 0
c = -4
(viii) y = x/2
Rearranging, x – 2y +0 = 0
On comparing with the given form of linear equation, ax + by + c = 0,
We get,
a = 1
b = -2
c = 0
Question 2: Write each of the following as an equation in two variables:
(i) 2x = -3
(ii) y=3
(iii) 5x = 7/ 2
(iv) y = 3/2x
Solution:
(i) 2x = -3
Rearranging,
2x + 3 = 0
Now adding ‘y’ term,
2x + 0.y + 3 = 0
Required equation is,
2x + 0.y + 3 = 0
(ii) y = 3
Rearranging,
y – 3 = 0
Now adding ‘x’ term,
0.x + y – 3 = 0
Required equation is,
0.x + y – 3 = 0
(iii) 5x = 7/2
Rearranging,
10x = 7,
or 10x – 7 – 0;
Now adding ‘y’ term,
10x +0.y – 7 = 0
Required equation is,
10x + 0.y – 7 = 0
(iv) y = 3/2 x
Rearranging,
2y = 3x
or 3x – 2y = 0
Now adding the constant term,
3x – 2y + 0 = 0
Required equation is,
3x – 2y + 0 = 0
Question 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 a ball pen and fountain pen be x and y respectively.
According to the question the following equation can be formed,
x = y/2 − 5
or x = (y – 10)/2
or 2x = y – 10
or 2x – y + 10 = 0
The required linear equation will be 2x – y + 10 = 0.
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