# NCERT Solutions for Class 9 Maths Exercise 4.2

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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 putin 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 putin 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 putin 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 putin 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 putin the linear equation, to get

Thus, we get third pair of solution as.

Let us putin 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 equationand which are not:

(i)

(ii)

(iii)

(iv)

(v)

Ans. (i)

We need to putin 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 putin 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 putin 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 putin 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 putin 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.

## NCERT Solutions for Class 9 Maths Exercise 4.2

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### 2 thoughts on “NCERT Solutions for Class 9 Maths Exercise 4.2”

1. Can you answer my question.
Q1,In ratio 11:14 , if the antecedent is 66, the consequent is?

2. Thanks