Exercise 4.2
NCERT solutions for Class 9 Maths Linear Equations in Two Variables
NCERT Solutions for Class 9 Mathematics Linear Equations in Two Variables
1. Which one of the following options is true, and why?
has
(i) a unique solution,
(ii) only two solutions,
(iii) infinitely many solutions
Ans. We need to the number of solutions of the linear equation.
We know that any linear equation has infinitely many solutions.
Justification:
If 
then 
If 
then 
If 
then 
= 
Similarly, we can find infinite many solutions by putting the values of 
NCERT Solutions for Class 9 Maths Exercise 4.2
2. Write four solutions for each of the following equations:
(i) 
(ii) 
(iii) 
Ans.
We know that any linear equation has infinitely many solutions.
Let us putin the linear equation, to get
Thus, we get first pair of solution as
.
Let us put
in the linear equation, to get
Thus, we get second pair of solution as
.
Let us put
in the linear equation, to get
Thus, we get third pair of solution as
.
Let us put
in the linear equation, to get
Thus, we get fourth pair of solution as
.
Therefore, we can conclude that four solutions for the linear equationare
.
(ii)
We know that any linear equation has infinitely many solutions.
Let us putin the linear equation, to get
Thus, we get first pair of solution as
.
Let us put
in the linear equation, to get
Thus, we get second pair of solution as
.
Let us putin the linear equation, to get
Thus, we get third pair of solution as
.
Let us put
in the linear equation, to get
Thus, we get fourth pair of solution as
.
Therefore, we can conclude that four solutions for the linear equationare
.
(iii)
We know that any linear equation has infinitely many solutions.
Let us putin the linear equation, to get
Thus, we get first pair of solution as
.
Let us putin the linear equation, to get
Thus, we get second pair of solution as
.
Let us put
in the linear equation, to get
Thus, we get third pair of solution as
.
Let us put
in the linear equation, to get
Thus, we get fourth pair of solution as
.
Therefore, we can conclude that four solutions for the linear equationare
.
NCERT Solutions for Class 9 Maths Exercise 4.2
3. Check which of the following are solutions of the equation
and which are not:
(i) 
(ii) 
(iii) 
(iv) 
(v) 
Ans. (i)
We need to put
in the L.H.S. of linear equation, to get
L.H.S. 
R.H.S.
Therefore, we can conclude thatis not a solution of the linear equation .
(ii)
We need to put
in the L.H.S. of linear equation, to get
L.H.S. R.H.S.
Therefore, we can conclude thatis not a solution of the linear equation .
(iii)
We need to put
in the linear equation, to get
L.H.S. 
R.H.S.
Therefore, we can conclude thatis a solution of the linear equation .
(iv)
We need to put
in the linear equation, to get
L.H.S. R.H.S.
Therefore, we can conclude thatis not a solution of the linear equation .
(v)
We need to put
in the linear equation, to get
L.H.S. R.H.S.
Therefore, we can conclude thatis not a solution of the linear equation .
NCERT Solutions for Class 9 Maths Exercise 4.2
4. Find the value of k, if x = 2, y = 1 is a solution of the equation
.
Ans. We know that, if 
is a solution of the linear equation, then on substituting the respective values of x and y in the linear equation , the LHS and RHS of the given linear equation will not be effected.
Therefore, we can conclude that the value of k, for which the linear equationhasas one of its solutions is 7.