# MCQs for Mathematics Class 10 with Answers Chapter 3 Linear Equations

Students of class 10 Mathematics should refer to MCQ Questions Class 10 Mathematics Linear Equations with answers provided here which is an important chapter in Class 10 Mathematics NCERT textbook. These MCQ for Class 10 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 10 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 10 Mathematics examination

**Chapter 3 Linear Equations MCQ with Answers Class 10 Mathematics**

MCQ Questions Class 10 Mathematics Linear Equations provided below have been prepared by expert teachers of grade 10. These objective questions with solutions are expected to come in the upcoming Standard 10 examinations. Learn the below provided MCQ questions to get better marks in examinations.

**Question. The value of x and y satisfying the system of equations 2x – 3y + 13 = 0 and 3x – 2y + 12 = 0 is : **

(a) x = 2, y = 3

(b) x = – 2, y = – 3

(c) x = – 2, y = 3

(d) none of these

**Answer**

C

**Question. The system of equations 3x – 2y = 7 and 7x + 8y = 12 has : **

(a) unique solution

(b) no solution

(c) infinitely many solutions

(d) can’t determine

**Answer**

A

**Question. The value of k for whcih the system of equations 2x + ky = 1, 3x – 5y = 7 has a unique solution, is : **

(a) k =−10/3

(b) k ≠− 10/3

(c) k = 0

(d) k ≠ 0

**Answer**

B

**Question. The value of x and y satisfying the system of equations 3x + y = – 1 and 2x – 3y = – 8 is: **

(a) x =1, y = – 2

(b) x = –1, y = 2

(c) x = 2, y = – 3

(d) none of these

**Answer**

B

**Question. If the system of equations 3x + y = 1, (2k – 1) x + (k – 1) y = 2k + 1 is inconsistent, then the value of k is: **

(a) 1

(b) 0

(c) –1

(d) 2

**Answer**

D

**Question. If 2x – 3y = 7 and (a + b) x – (a + b – 3) y = 4a + b represent coincident lines, then a and b satisfy the equation: **

(a) 5a + b = 0

(b) a – 5b = 0

(c) a + 5b = 0

(d) 5a – b = 0

**Answer**

B

**Question. The value of x and y satisfying the systems of equations 57/x=y+6/ x-y=5 and 38 /x+ y + x- y = 9 is **

(a) x = 11, y = – 8

(b) x = – 11, y = 8

(c) x = 11, y = 8

(d) none of these

**Answer**

C

**Question. The value of k for which the system of equations 3x – 2y = 8, 6x – ky = 16 has infinitely many solutions, is **

(a) k = 1

(b) k = 2

(c) k = 3

(d) k = 4

**Answer**

D

**Question. The value of x and y satisfying the system of equations x /a+y/b =2 and ax – by = a ^{2} – b^{2} is : **

(a) x = a, y = b

(b) x = – a, y = – b

(c) x = a

^{2}, y = b

^{2}

(d) none of these

**Answer**

A

**Question. The value of k for which the system of equations x + 2y = 3 and 5x + ky + 7 = 0 has no solution, is : **

(a) 1

(b) 10

(c) 3

(d) 6

**Answer**

B

**Question. The pair of equations x +2y + 5 = 0 and – 3x – 6y + 1 = 0 have **

(a) a unique solution

(b) exactly two solutions

(c) infinitely many solutions

(d) no solution

**Answer**

D

**Question. The value of c for which the pair of equation cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is **

(a) 3

(b) –3

(c) –12

(d) no value

**Answer**

D

**Question. A pair of linear equations which has a unique solution x = 3, y = –2 is **

(a) x+ y =1

2x – 3y = 12

(b) 2x+ 5y+4=1

4x 10y+8=0

(c) 2x- y=1

3x+2y=0

(d) x -4y=14

5x – y=13

**Answer**

A

**Question. For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = – 16 represent coincident lines? **

(a) 1/2

(b) –1/2

(c) 2

(d) –2

**Answer**

C

**Question. The area of the triangle formed by the line a x b y + = 1 with the coordinate axes is **

(a) ab

(b) 2ab

(c) ab 2 1

(d) ab 4 1

**Answer**

C

**Question. If 2x – 3y = 7 and (a + b)x – (a + b – 3)y = 4a + b represent coincident lines, then a and b satisfy the equation **

(a) a + 5b = 0

(b) 5a + b = 0

(c) a – 5b = 0

(d) 5a – b = 0

**Answer**

C

**Question. The pair of linear equations 4x + 6y = 9 and 2x + 3y = 6 has **

(a) no solution

(b) many solutions

(c) two solutions

(d) one solution

**Answer**

A

**Question. The pair of equations y = 0 and y = –7 has **

(a) one solution

(b) two solutions

(c) infinitely many solutions

(d) no solution

**Answer**

D

**Question. The pair of equations x = a and y = b graphically represents lines which are **

(a) parallel

(b) intersecting at (b, a)

(c) coincident

(d) intersecting at (a, b)

**Answer**

D

**Question. Two numbers are in the ratio 1 : 3. If 5 is added to both the numbers, the ratio becomes 1 : 2. The numbers are **

(a) 4 and 12

(b) 5 and 15

(c) 6 and 18

(d) 7 and 21

**Answer**

B

**Question. Point (4, 3) lies on the line **

(a) 3x + 7y = 27

(b) 7x + 2y = 47

(c) 3x + 4y = 24

(d) 5x – 4y =1

**Answer**

C

**Question. A boat can row 1 km with stream in 10 minutes and 1 km against the stream in 20 minutes. The speed of the boat in still water is **

(a) 1.5 km/h

(b) 3 km/h

(c) 3.4 km/h

(d) 4.5 km/h

**Answer**

D

**Question. Gunjan has only ™ 1 and ™ 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is ™ 75, then the number of ™ 1, and ™ 2 coins are respectively **

(a) 25 and 25

(b) 15 and 35

(c) 35 and 15

(d) 35 and 20

**Answer**

A

**Question. Find the values of x and y if ABCD is a cyclic quadrilateral, ∠A = 6x + 10°, ∠B = (5x)°, ∠C = (x+ y)° (∠D)=(3y-10)°. **

(a) x = 30°, y = 20°

(b) x = 20°, y = 30°

(c) x = 40°, y = 10°

(d) x = 10°, y = 40°

**Answer**

B

**Question. If x = a and y = b is the solution of the (a) coincident .equations + 3y = 14 and – 4y = 23,then the values of a and b are respectively: **

(a) – 2 and 5

(b) 5 and – 2

(c) and – 2

(d) 5 and –1/2

**Answer**

C

**Question. Find p and q so that given system has infinite number of solutions, 4x + 6y -14 = 0. ****(p + q)x + (2 p – q)y – 3 (p + q +1) = 0**

(a)p = 1, q = 1

(b)p = 1,q = – 1

(c) p = 1, q = 5

(d) p = 5, q = 1

**Answer**

D

**Question. Find the solution to the following system of linear equations: 2x-5y+4 = 0 2x+y-8 = 0? **

(a) (3,-2)

(b) (2,3)

(c) (-1,2)

(d) (3,2)

**Answer**

D

**Question. Find x and y in the given rectangle : **

(a) x = 1, y = 4

(b) x = 4, y = 1

(c) x = 2, y = 2

(d) x = 3, y = 1

**Answer**

A

**Question. Two equations in two variables taken together are called **

(a) linear equations

(b) quadratic equations

(c) simultaneous equations

(d) none of these

**Answer**

C

**Question. If the pair of equation has no solution, then the pair of equation is : **

(a) inconsistent

(b) coincident

(c) consistent

(d) none of these

**Answer**

A

**Question. If x = a, y = b is the solution of the equations x + y = 5 and 2x – 3y = 4, then the values of a and bare respectively **

(a) 6, -1

(b) 2, 3

(c) 1, 4

(d) 19/5,6/5

**Answer**

D

**Question. Find the value of ‘a” for which the system of equations ax + 2y – 4 = 0 and x – y – 3 = 0 willrepresent intersecting lines? **

(a) a ≠ -2

(b) a = -2

(c) a = 2

(d) a ≠ 2

**Answer**

A

**Question. The pair of equations 3x + 4y = k, 9x + 12y = 6 has infinitely many solutions if – **

(a) k = 2

(b) k = 6

(c) k = 6

(d) k = 3

**Answer**

A

**Question. One equation of a pair of dependent linear equations is -5x + 7y = 2. The second equation can be: **

(a) 10x + 14y + 4 = 0

(b) – 10x – 14y + 4 = 0

(c) – 10x + 14y + 4 = 0

(d) 10x – 14y = – 4

**Answer**

D

**Question. If a pair of linear equations is consistent, then the lines will be **

(a) always coincident

(b) parallel

(c) always intersecting

(d) intersecting or coincident

**Answer**

D

**Question. The pair of equations y = 0 and y = – 7 has : **

(a) no solution

(b) infinitely many solutions

(c) one solution

(d) two solutions

**Answer**

A

**Question. The pair of equations 3x – 5y = 7 and – 6x + 10y = 7 have **

(a) a unique solution

(b) infinitely many solutions

(c) no solution

(d) two solutions

**Answer**

C

**Question. The graph of y = 5 is a line parallel to the **

(a) x-axis

(b) y-axis

(c) both axis

(d) none of these

**Answer**

A

**Question. The value of k, for which equations 3x + 5y = 0 and kx + lOy = 0 has a non-zero solution is **

(a) 6

(b) 0

(c) 2

(d) 5

**Answer**

A

**Question. Which of following is not a solution of 3a + b = 12 ? **

(a) (3, 3)

(b) (5, -3)

(c) (4, 0)

(d) (2, 4)

**Answer**

D

**Question. 8 girls and 12 boys can finish work in 10 days while 6 girls and 8 boys can finish it in 14 days.Find the time taken by the one girl alone that by one boy alone to finish the work. **

(a) 120, 130

(b) 140,280

(c) 240,280

(d) 100,120

**Answer**

B

**Question. The graph of y = 4x is a line **

(a) parallel to x-axis

(b) parallel to y-axis

(c) perpendicular to y-axis

(d) passing through the origin

**Answer**

D

**Question. Which of the following is not a solution of pair of equations 3x – 2y = 4 and 6x – 4y = 8? **

(a) x = 5, y = 3

(b) x = 2, y = 1

(c) x = 6, y = 7

(d) x = 4, y = 4

**Answer**

A

**Question. How many solutions of the equation 15x – 14y + 11 = 0 are possible? **

(a) 2

(b) No solution

(c) 1

(d) Infinite

**Answer**

D

**Question. Find a and b for which (a – 1) x + 3y = 2, 6x + (1 – 2b) y = 6 infinite solution.? **

(a) a = -7, b= -4

(b) a = -1, b = -4

(c) a = 3, b = -1

(d) a = 3, b = -4

**Answer**

D

**Question. If am bl then the system of equations ax + by = c, lx + my = n, has **

(a) a unique solution

(b) no solution

(c) infinitely many solutions

(d) none of these

**Answer**

A

**Question. Find the solution to the following system of linear equations: 2p+3q = 9 p – q = 2? **

(a) (4,2)

(b) (3,1)

(c) (2,-3)

(d) (-4,1)

**Answer**

B

**Question. The present age of a father is the sum of the ages of his three sons. Ten years from now his agewill be a three quarter of the sum of their ages then. How old is the father? **

(a) 50 years

(b) 30 years

(c) 40 years

(d) 60 years

**Answer**

A

**Question. The pair of equations 5x – 15y = 8 and 3x-9y =24/5 has **

(a) one solutio

(b) two solutions

(c) infinitely many solutions

(d) no solution

**Answer**

C

**Question. ` 49 was divided among 150 children. Each girl got 50 paise and each boy got 25 paise. How many boys were there? **

(a) 100

(b) 102

(c) 104

(d) 105

**Answer**

C

**Question. A boat takes 3 hours to travel 30 km downstream and takes 5 hours to return to the same spot upstream. Find the speed of the boat in still water. (km/hr) **

(a) 10 km/hr

(b) 8 km/hr

(c) 6 km/hr

(d) 5 km/hr

**Answer**

B

**Question. If the sum of the ages (in years) of a father and his son is 65 and twice the difference of their ages (in years) is 50, what is the age of the father? **

(a) 45 years

(b) 40 years

(c) 50 years

(d) 55 years

**Answer**

A

**Question. The value of k for which the system of linear equations x + 2y = 3, 5x + ky + 7 = 0 is inconsistent is **

(a) −14/ 3

(b) 2/ 5

(c) 5

(d) 10

**Answer**

D

**Question. The points (7, 2) and (–1, 0) lie on a line **

(a) 7y = 3x – 7

(b) 4y = x + 1

(c) y = 7x + 7

(d) x = 4y + 1

**Answer**

B

**Question. In a classroom, one-fifth of the boys leave the class and the ratio of the remaining boys to girls is 2 : 3. If further 44 girls leave the class, then the ratio of boys to girls is 5: 2. How many more boys should leave the class so that the number of boys equals that of girls? **

(a) 16

(b) 24

(c) 30

(d) 36

**Answer**

B

**Question. The perimeter of a rectangle is 40 cm. The ratio of its sides is 2 : 3. Find its length and breadth. **

(a) l = 10 cm, b = 8 cm

(b) l = 12 cm, b = 8 cm

(c) l = 12 m, b = 8 m

(d) l = 40 m, b = 30 m

**Answer**

B

**Question. The equations 1/x +1/y =15 and 1/x – 1/y= 5 are such that ax = 1 and by = 1. The values of ‘a’ and ‘b’ respectively are **

(a) 10, 5

(b) 10, –5

(c) –5, 10

(d) 5, 10

**Answer**

A

**Question. At present ages of a father and his son are in the ratio 7 : 3, and they will be in the ratio 2 : 1 after 10 years. Then the present age of father (in years) is **

(a) 42

(b) 56

(c) 70

(d) 77

**Answer**

C

**Question. The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is **

(a) 25

(b) 72

(c) 63

(d) 36

**Answer**

D

**Question. A fraction becomes 4 when 1 is added to both the numerator and denominator and it becomes 7 when 1 is subtracted from both the numerator and denominator. The numerator of the given fraction is **

(a) 2

(b) 3

(c) 5

(d) 15

**Answer**

D

**Question. A can do a piece of work in 24 days. If B is 60% more efficient than A, then the number of days required by B to do the twice as large as the earlier work is **

(a) 24

(b) 36

(c) 15

(d) 30

**Answer**

D

**Question. A motor boat takes 2 hours to travel a distance 9 km down the current and it takes 6 hours to travel the same distance against the current. The speed of the boat in still water and that of the current (in km/hour) respectively are **

(a) 3, 1.5

(b) 3, 2

(c) 3.5, 2.5

(d) 3, 1

**Answer**

A

**Question. For which value of p, will the lines represented by the following pair of linear equations be parallel **

3x – y – 5 = 0

6x – 2y – p = 0

(a) all real values except 10

(b) 10

(c) 5/2

(d) 1/2

**Answer**

A

**Question. The 2 digit number which becomes (5/6)th of itself when its digits are reversed. The difference in the digits of the number being 1, then the two digits number is **

(a) 45

(b) 54

(c) 36

(d) None of these

**Answer**

B

**Question. The pair of linear equations x + 2y = 5 and 3x + 12y = 10 has **

(a) unique solution

(b) no solution

(c) more than two solutions

(d) infinitely many solutions

**Answer**

A

**Question. x and y are 2 different digits. If the sum of the two digit numbers formed by using both the digits is a perfect square, then value of x + y is **

(a) 10

(b) 11

(c) 12

(d) 13

**Answer**

B

**Question. Which of the following is the other name for a pair of linear equations in two variables? **

(a) Consistent equations

(b) Simultaneous equations

(c) Inconsistent equations

(d) Dependent equations

**Answer**

B

**Question. For what values of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines? **

(a) solution of 3k – 9 = 0

(b) solution of 2k – 8 = 0

(c) 2

(d) 3

**Answer**

C

**Question. A man can row a boat in still water at the rate of 6 km per hour. If the stream flows at the rate of 2 km/hr, he takes half the time going downstream than going upstream the same distance. His average speed for upstream and down stream trip is **

(a) 6 km/hr

(b) 16/3 km/hr

(c) Insufficient data to arrive at the answer

(d) none of the above

**Answer**

B

**Question. X’s salary is half that of Y’s. If X got a 50% rise in his salary and Y got 25% rise in his salary, then the percentage increase in combined salaries of both is **

(a) 30

(b) 33, 1/ 3

(c) 37, 1/ 2

(d) 75

**Answer**

B

**Question. A boat travels with a speed of 15 km/hr in still water. In a river flowing at 5 km/hr, the boat travels some distance downstream and then returns. The ratio of average speed to the speed in still water is **

(a) 8 : 3

(b) 3 : 8

(c) 8 : 9

(d) 9 : 8

**Answer**

C

**Question. If the length of a rectangle is increased by 2 m and breadth is reduced by 2 m, its area decreases by 28 sq. m. If the length is reduced by 1 m and the breadth is increased by 2 m, the area increases by 33 sq m. Find the actual measurements of the rectangle. **(a) l =13m,b =11 m

(b) l = 23 m, b = 11 m

(c) l = 23m,b = 20m

(d) l =12 m, b = 10 m

**Answer**

B

**Question. What is a system of simultaneous equations called if its graph has intersecting lines? **(a) Inconsistent system

(b) Consistent system

(c) Dependent system

(d) Independent system

**Answer**

B

**Question. If the pair of linear equations 3x + 5y = 3 and 6x + ky = 6 do not have any solution, which of the following is true? **

(a) k = 5

(b) k=10

(c) k ≠10

(d) k ≠ 5

**Answer**

B

**Question. Two numbers are in the ratio 2 :7. If 6 is added to each of the numbers, the ratio becomes 1 :3. Find the numbers. **(a) 14, 49

(b) 16, 56

(c) 18, 63

(d) 24, 84

**Answer**

D

**Question. Which of the following is a consistent system of simultaneous equations? **

(a) m+3n = 6 , 2m+6n =12

(b) a + 3b = 6 , 2a – 3b =12

(c) x – 4y = 6 , 2x – 8y =12

(d) l – 2m= 6 , 3l – 6m =12

**Answer**

B

**Question. If 3x + 5y = 5and x/x + y = 5/7 , what is the value of x – y ? **

(a) 9

(b) 6

(c) 4

(d) 3

**Answer**

D

**Question. For the equations (p +2)(q – 1/2) = pq – 5 and (p – 2)(q – 1/2) = pq – 5 , find the solution set (p, q). **

(a) (- 10 , – 1/2)

(b) (- 10 , 1/2)

(c) (10 , – 1/2)

(d) (10 , 1/2)

**Answer**

D

**Question. Identify the solution of 2/3 x – 3/4 y = 1 and 8x – 9y =16. **

(a) x = 6,y = 4

(b) Infinitely many solutions

(c) x = 4,y = 6

(d) No solution

**Answer**

D

**Question. What is the nature of the graphs of a system of linear equations with exactly one solution? **

(a) Parallel lines

(b) Perpendicular lines

(c) Coincident lines

(d) Intersecting lines

**Answer**

D

**Question. What is the number of solutions of the pair of linear equations 4p – 6q +18 = 0 and 2p – 3q + 9 = 0 ? **

(a) 0

(b) 1

(c) 2

(d) Infinitely many

**Answer**

D

**Question. x and y are two non-negative numbers such that 2x + y = 10. The sum of the maximum and minimum values of (x + y) is **

(a) 6

(b) 9

(c) 10

(d) 15

**Answer**

D

**Question. The difference between two numbers is 26 and one number is three times the other. Find them. **

(a) 39, 13

(b) 41, 67

(c) 96, 70

(d) 52, 26

**Answer**

A

**Question. The graphs of the equations x – y = 2 and kx + y = 3, where k is a constant, intersect at the point (x, y) in the first quadrant, if and only if k is **

(a) equal to –1

(b) greater than –1

(c) less than 3/2

(d) lying between –1 and 3/2

**Answer**

D

**Question. For what values of k will the following pair of linear equations have infinitely many solutions? **

kx + 3y – (k – 3) = 0

12x + ky – k = 0

(a) k = 4

(b) k = 3

(c) k = 6

(d) k = 2

**Answer**

C

**Question. If a pair of linear equations is inconsistent, then the lines will be **

(a) parallel

(b) always coincident

(c) intersecting

(d) coincident

**Answer**

A

**Question. If 3x + 4y : x + 2y = 9 : 4, then 3x + 5y : 3x – y is equal to **

(a) 4 : 1

(b) 1 : 4

(c) 7 : 1

(d) 1 : 7

**Answer**

C

**Question. Which of the following is true if following pair of linear equations has unique solution? ****3x – 2y = – 8****(2m – 5)x + 7y – 6 = 0**

(a) m =11/4

(b) m =-11/4

(c) m ≠-11/4

(d) m ≠11/4

**Answer**

C

We hope the above multiple choice questions for Class 10 Mathematics for Chapter 3 Linear Equations provided above with answers based on the latest syllabus and examination guidelines issued by CBSE, NCERT and KVS are really useful for you. Linear Equations is an important chapter in Class 10 as it provides very strong understanding about this topic. Students should go through the answers provided for the MCQs after they have themselves solved the questions. All MCQs have been provided with four options for the students to solve. These questions are really useful for the benefits of class 10 students. Please go through these and let us know if you have any feedback in the comments section.