Top 10 Questions l Pair of Linear Equations in Two Variables

Top 10 Questions – Pair of Linear Equations in Two Variables

Class 10 Mathematics

Question 1

For which value(s) of k, do the pair of linear equations:

kx + y = k²

x + ky = 1

have:

1. No solution?
2. Infinitely many solutions?
3. A unique solution?

Question 2

Draw the graphs of the equations:

x = 3

x = 5

2x – y – 4 = 0

Also, find the area of the quadrilateral formed by these lines and the x-axis.

Question 3

If:

3^(x+y) = 81

81^(x+y) = 3

Find the value of (x + y).

Question 4

Solve the pair of linear equations:

αx + βy = α − β

βx − αy = α + β

Question 5

In a competitive examination, 4 marks are awarded for each correct answer while 1 mark is deducted for every wrong answer.

Anurag answered 120 questions out of 150 and got 360 marks. How many questions did she answer correctly?

Question 6

If:

2x − 3y = 7

(a + b)x − (a + b − 3)y = 4a + b

represent coincident lines, find the relation between a and b.

Question 7

Solve:

2/√α + 3/√β = 2

4/√α − 9/√β = −1

where α, β > 0

Question 8

If:

2^(2x−y) = 16

7^(x−2y) = 49

Find the value of x.

Question 9

If the system of equations:

px + 3y = p − 3

12x + py = p

has no solution, find the value of p.

Question 10

Find the value of k for which the equations:

kx + 3y = k − 3

12x + ky = k

have infinitely many solutions.

Chapter: Pair of Linear Equations in Two Variables

Class: 10