# CBSE Class 10 Maths Pair of Linear Equations in Two Variables | Chapter 3 MCQ

CBSE CLASS 10 MATHEMATICS/ MCQ | Multiple Choice Questions / Pair of Linear Equations in Two Variables –Chapter 3

1. An equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers and a and b are not both zero is called a ———————-

A. Linear equation

B. Quadratic equation

C. Cubic equation

2. Which of the following is a solution of the linear equation 2x + 3y = 5?

A. x = 0, y = 1

B. x = 1, y =1

C. x =1, y = 0

3. A pair of linear equations which has no solution is called an ———- pair oflinear equations.

A. Consistent

B. Inconsistent

C. Congruent

4. A pair of linear equations in two variables which has a solution is called a ——-pair of linear equations.

A. Consistent

B. Inconsistent

C. Similar

5. Dependent pair of linear equations is always —————-

A. Consistent

B. Inconsistent

C. Congruent

6. Graphically the pair of equations 2x + 4y – 12 = 0 and x + 2y – 4 = 0 represents two lines which are —————-

A. Intersecting at one point

B. Intersecting at two points

C. Parallel

7. If two lines intersect in a single point, then the pair of equations has a —— solution.

A. Unique

B. No

C. Infinitely many solutions

8. If two lines are parallel, the equations have ———– solution.

A. Unique

B. No

C. Infinitely many solutions

9. The following pair of linear equations 3x + 2y = 5 and 2x – 3y = 7 are ———

A. Inconsistent

B. Consistent

C. Congruent

10. Half the perimeter of a rectangular garden, whose length is 4m more than its width, is 36 m, then the dimensions of the garden is —————-

A. l = 20m, b = 16m

B. l = 16m, b= 20m

C. l = 18m, b = 18m

11. If the difference between two numbers is 26 and one number is three times the other, then the numbers are —————-

A. x = 36, y= 10

B. x = 39, y = 13

C. x = 33, y = 7

12. Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. Then their present ages are —————

A. x = 43, y = 13

B. x = 40, y= 10

C. x = 37, y = 7

13. The value of k is —— if the following pair of linear equations has no solution.

3x + y = 1 & (2k -1)x + (k-1)y = 2k +1

A. k = 1

B. k = 2

C. k = 3

14. The pair of equations 3x – y = 3 and 9x – 3y = 9 have ————

A. Unique solution

B. No solution

C. Infinitely many solutions

15. If a pair of linear equations is consistent, then the lines will be ———-

A. Parallel

B. Intersecting or coincident

C. Not intersecting, not parallel

ANSWERS:

1. Linear equations

2. x = 1, y =1

3. Inconsistent

4. Consistent

5. Consistent

6. Parallel

7. Unique

8. No

9. Consistent

10. l = 20m, b = 16m

Half the perimeter of a rectangle = l + b = 36m (given)

Let the width be b then length will be 4 +b.

Then 4 + b + b = 36

4 + 2b = 36

2b = 36 – 4 = 32

b= 32/2 = 16 and l = 4 + b = 4 + 16 = 20

11. x = 39, y = 13

Let the numbers be x and y.

Then the equations are x – y = 26, x = 3y.

12. x = 40, y = 10

Let x and y be the ages in years of Jacob and his son.

The equations are x +5 = 3(y + 5)

x + 5 = 3y + 15

x – 3y – 10 = 0 ———– (i)

x – 5 = 7 (y-5)

x – 5 = 7y – 35

x – 7y + 30 = 0 —————–(ii)

13. k = 2

14. Infinitely many solutions

15. Intersecting or coincident