- What is Linear equations
- |
- Linear equations Solutions
- |
- Graphical Representation of Linear equation in one and two variable
- |
- Steps to Draw the Given line on Cartesian plane
- |
- Simultaneous pair of Linear equation
- |
- Algebraic Solution of system of Linear equation
- |
- Simultaneous pair of Linear equation in Three Variable
- |
- Steps to solve the equations

- -1">
- Problem and Solutions
- |
- Linear equations Problems
- |
- Linear equation worksheet
- |
- Linear equation word problems
- |
- Linear equations graphical problems

Given below are the

a) Concepts questions

b) Calculation problems

c) Multiple choice questions

d) Long answer questions

e) Fill in the blank's

1) In a cyclic quadrilateral ABCD, Find the four angles.

a) <A = (2x + 4), <B = (y + 3), <C = (2y + 10), <D = (4x -5).

b) <A = (2x – 1), <B = (y + 5), <C = (2y + 15) and <D = (4x -7). c) <A = (2x – 1), <B = (y + 5) ,<C = (2y + 15) and <D = (4x – 7).

d) <A = (2x + 4), <B = (y + 3), <C = (2y + 10), <D = (4x – 5).

2) Given below are three equations. Two of them have infinite solutions and two have a unique solution. State the two pairs:

3x – 2y = 4

6x + 2y = 4

9x -6y = 12.

3) Find the values of a and b for which the following system of linear equations has infinite number of solutions:

2x + 3y = 7; 2ax + (a + b)y = 28.

4) Find the values of a and b for which the following system of linear equations has infinite number of solutions:

2x -3y = 7; (a + b)x – (a + b- 3)y = 4a + b.

5) In a ABC, <A = x, <B = (3x -2), <C = y. Also <C - <B = 9. Find the three angles.

6) Find the value of k for which the system of equations x + 2y – 3 = 0 and ky + 5x + 7 = 0 has a unique solution.

7) For what value (s) of ‘a’, the system of linear equations 2x + 3y = 7 and (a – 1)x + (a + 1)y = 3a + 1 represent parallel lines.

8) If the lines x + 2y + 7 = 0 and 2x + ky + 18 = 0 intersect at a point, then find the value of k.

9) Is x = 5, y = -5 a solution of the linear equation 3x + 2y – 5 = 0?

10) The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. Find the present ages of the son and the father.

11) Replace ‘p’ by an appropriate number so that the following system of equations has a unique solution.

2x + 3y = 5

px +9y = 12

12) For what value of k, the following pair of linear equations has infinitely many solutions?

i) kx + 4y – (k + 8) = 0

4x + ky + 4 = 0

ii) 2x + 3y = 4

(k + 2)x + 6y = 3k + 2

13) For what value of k, will the following system of equations have no solutions?

i) (3k + 1) x + 3y = 2; (k

ii)

3x + y = 1

(2k – 1) x + (k – 1) y = 2k + 1

iii)

2x + ky = 11

5x – 7y = 5

2x + ky = 6, 4x + 6y = 0

15) Find the value of k for which the following system of linear equations has infinite solutions:

i) x + (k + 1) y = 5

(k + 1) x + 9y = 8k – 1

ii)

8x + 5y = 9

kx + 10y = 18

iii) 2x + 3y = k

(k – 1) x + (k + 2) y = 3k

16) For what value of α, the system of equations

αx + 3y = α – 3

12x + αy = α

will have no solution?

17) Find the value of k for which the system

kx + 2y = 5

3x + y = 1

has (i) a unique solution, and (ii) no solution.

18) Find the value of k for which the system

2x + ky = 1

3x – 5y = 7

has (i) a unique solution, and (ii) no solution.

19 )find the value of a and b for which the following system of equations has infinitely many solutions:

2x – (2a + 5) y = 5

(2b + 1) x – 9y = 15

20) Find the value of a for which the following system of equations has infinitely many solutions:

2x + 3y – 7 = 0

(a – 1) x + (a + 1) y = (3a – 1)

Answer

1)

ii) 65, 55, 115, 125

iii) 65, 55, 115, 125.

iv) 10, 53, 110, 127

2) 1 & 3, 1 & 2

3) 4,8

4) -5,-1

5) 25,73, 82

6) k ≠ 10

7) 5

8) k ≠ 4

9) Yes

16) -6

17) k≠6 , k=6

18) k≠ -10/3 , k=10/3

19) (-1, 5/2)

20) a=5

Go Back to Class 10 Maths Home page Go Back to Class 10 Science Home page

- Mathematics (Class 10) by RD Sharma
- NCERT Solutions - Mathematics Class 10
- NCERT Exemplar Mathematics Problems - Solutions (Class 10)
- Board + IIT - JEE Foundation Mathematics (Class 10) by disha experts
- Mathematics Foundation Course for JEE/AIPMT/Olympiad Class : 10 (by mtg)
- Board + PMT/ IIT Foundation for JEE Main / Advanced: Science & Mathematics, Class - 10
- Class Companion - Class 10 Mathematics