# NCERT Mathematics Class 10 Exemplar Ch 3 Pair of Linear Equations in Two Variables Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**EXERCISE 3.3**

1. For which value (s) of λ , do the pair of linear equations and have

(i) no solution?

(ii) infinitely many solutions?

(iii) a unique solution?

Answer: (i) (ii) (iii) All real values of λ except + 1.

2. For which value (s) of k will the pair of equations have no solution?

Answer:

3. For which values of a and b, will the following pair of linear equations have infinitely many solutions? ,

Answer: ,

4. Find the value (s) of p in (i) to (iv) and p and q in (v) for the following pair of equations:

(i) and

if the lines represented by these equations are parallel.

(ii) and , if the pair of equations has no solution.

(iii) and if the lines represented by these equations are intersecting at a unique point.

(iv) and , if the pair of equations has a unique solution.

(v) and , if the pair of equations have infinitely many solutions.

Answer: (i) All real values of p except 10.

(ii)

(iii) All real values of p except 9 10 .

(iv) All real values of p except – 4.

(v)

5. Two straight paths are represented by the equations and Check whether the paths cross each other or not.

Answer: Do not cross each other.

6. Write a pair of linear equations which has the unique solution , . How many such pairs can you write?

Answer:

; infinitely many pairs.

7. If and , find the values of and

Answer: ,

8. Find the values of x and y in the following rectangle [see Fig. 3.2] .

Answer: ,