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Class IX Chapter 13 – Linear Equations in Two Variables Maths______________________________________________________________________________
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) 2 x 3 y 12 (v) 2x + 3 = 0
y (vi) y–5=0
(ii) x 5 0
2 (vii) 4 = 3x
𝑥
(iii) 2 x 3 y 9 35 (viii) 𝑦=2
(iv) 3 x 7 y
Sol:
(i) We have
2 x 3 y 12
2 x 3 y 12 0
On comparing this equation with ax by c 0 we obtain a 2, b 3 and c 12 .
(ii) Given that
y
x 5 0
2
y
1x 5 0
2
1
On comparing this equation with ax by c 0 we obtain a 1, b and c 5
2
(iii) Given that
2 x 3 y 9 35
2 x 3 y 9 35 0
On comparing this equation with ax by c 0 we get a 2, b 3 and c 9 35
(iv) 3x 7 y 3x 7 y 0 0
On comparing this equation with ax by c 0 we get a 3, b 7 and c 0 .
(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
0 x 1y 5 0
On comparing this equation with ax by c 0 we get a 0, b 1 and c 5
,Class IX Chapter 13 – Linear Equations in Two Variables Maths
______________________________________________________________________________
(vii) We have
4x
3 x 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,
x
y
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
7
(iii) 5x = 2
3
(iv) y = 2𝑥
Sol:
(i) We have
2 x 3
2x 3 0
2x 0 y 3 0
(ii) We have,
y3
y 3 0
0 x 1 y 3 0
(iii) Given
7
5x
2
10 x 7 0
10 x 0 y 7 0
(iv) We have
3
y x
2
3x 2 y 0
3x 2 y 0 0
,Class IX Chapter 13 – Linear Equations in Two Variables Maths
______________________________________________________________________________
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.
Sol:
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
y
x 5
2
2 x y 10
2 x y 10 0
Exercise – 13.2
1. Write two solutions for each of the following equations:
(i) 3x + 4y = 7
(ii) x = 6y
(iii) x + 𝜋y = 4
2
(iv) 𝑥−𝑦 =4
3
Sol:
(i) Given that 3 x 4 y 7
Substituting x 0 in this equation, we get
3 0 4 y 7
7
y
4
7
So, 0, is a solution of the given equation substituting x 1, in given equation, we
4
get
3 1 4 y 7
4y 7 3
4
y 1
So, 1,1 is a solution of the given equation
7
0, and 1,1 are the solutions for the given equation.
4
(ii) We have
x 6y
Substituting y 0 in this equation, we get x 6 0 0
, Class IX Chapter 13 – Linear Equations in Two Variables Maths
______________________________________________________________________________
So, 0, 0 is a function of the given equation substituting y 1, in the given equation, we
set x 6 1 6
So, 6,1 is a solution of the given equation.
we obtain 0, 0 and 6,1 as solutions of the given equation.
(iii) We have
x y 4
Substituting y 0 in this equation, we get
x 0 4
x4
So, y , 0 is a solution of the give equation.
we obtain 4, 0 and 4 x as solutions of the given equation.
(iv) Given that
2
x y 4
3
Substituting y 0 in this equation we get
2
x0 4
3
3
x 4
2
x6
So, 6, 0 is a solution of the given equation
Substituting y 1 in the given equation, we get
2
1 4
3
2 15
x 5 x
3 2
15
So, ,1 is a solution of the given equation.
2
15
We obtain 6, 0 and ,1 as solutions of the given equation.
2
2. Write two solutions of the form x = 0, y = a and x = b, y = 0 for each of the following
equations:
(i) 5x – 2y = 10 (ii) −4x + 3y = 12 (iii) 2𝑥 + 3𝑦 = 24
Sol:
(i) Given that
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