Students can refer to the following linear equations class 10 MCQ Question with Answers provided below based on the latest curriculum and examination pattern issued by CBSE and NCERT. Our teachers have provided here collection of multiple choice questions for Linear Equations Class 10 covering all topics in your textbook so that students can assess themselves on all important topics and thoroughly prepare for their exams

## linear equations class 10 MCQ Question with Answers

We have provided below linear equations class 10 MCQ Question with answers which will help the students to go through the entire syllabus and practice multiple choice questions provided here with solutions. As Linear Equations MCQs in Class 10 pdf download can be really scoring for students, you should go through all problems and MCQ Questions for Class 10 Maths provided below so that you are able to get more marks in your exams.

#### linear equations class 10 MCQ Question

**Question. The pair of equations 6x -7y =1 and 3x – 4 y = 5 has **

(a) a unique solution

(b) two solutions

(c) infinitely many solutions

(d) no solution

**Answer**

A

**Question. The pair of equations 4x -3y +5 = 0 and 8x -6 y -10 = 0 graphically represents two lines which are **

(a) coincident

(b) parallel

(c) intersecting at exactly one point

(d) intersecting at exactly two points

**Answer**

B

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

(a) intersecting at (a, b)

(b) intersecting at (b, a)

(c) parallel

(d) coincident

**Answer**

C

**Question. Divya has only ≠ 2 and ≠ 5 coins with her. If the total number of coins that she has is 25 and the amount of money with her is ≠ 80, then the number of ` 2 and ≠ 5 coins are , respectively **

(a) 15 and 10

(b) 10 and 15

(c) 12 and 10

(d) 13 and 12

**Answer**

B

**Question. A pair of linear equations which has x = 0, y = -5 as a solution is **

(a) x+y=0/2x-3y=10

(b) x+y=3/2x-y=5

(c) 2x+3y+5=0/3x+2y=0/x-4y=0

(d) x-4y=14/5x-y=13

**Answer**

C

**Question. The number of solutions of the pair of linear equations x +3y – 4 = 0 and 2x +6 y = 7 is **

(a) 0

(b) 1

(c) 2

(d) infinite

**Answer**

A

**Question. A’s age is six times B’s age. Four years hence, the age of A will be four times B’s age. The present ages, in years, of A and B are, respectively **

(a) 3 and 24

(b) 36 and 6

(c) 6 and 36

(d) 4 and 24

**Answer**

B

**Question. The value of k for which the lines (k +1)x +3ky +15 = 0 and 5x + ky +5 = 0 are coincident is **

(a) 14

(b) 2

(c) –14

(d) –2

**Answer**

A

**Question. The pair of equations x = 2 and y = 3 has **

(a) one solution

(b) two solutions

(c) many solutions

(d) no solution

**Answer**

A

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

(a) parallel

(b) always coincident

(c) intersecting or coincident

(d) always intersecting

**Answer**

A

**Question. If a pair of linear equations has infinitely many solutions, then the lines representing them will be **

(a) parallel

(b) intersecting or coincident

(c) always intersecting

(d) always coincident

**Answer**

A

**Question. The value of k for which the pair of equations kx + y = 3 and 3x +6 y = 5 has a unique solution is **

(a) – 1/2

(b) 2

(c) –2

(d) all the above

**Answer**

D

**Question. The number of solutions of the pair of equations 2x +5y =10 and 6x +15y -30 = 0 is **

(a) 0

(b) 1

(c) 2

(d) infinite

**Answer**

D

**Question. The value of k for which the system of equations x +3y – 4 = 0 and 2x + ky = 7 is inconsistent is **

(a) 21/4

(b) 1/6

(c) 6

(d) 4/21

**Answer**

C

**Question. Sanya’s age is three times her sister’s age. Five years hence, her age will be twice her sister’s age. The present ages (in years) of Sanya and her sister are respectively **

(a) 12 and 4

(b) 15 and 5

(c) 5 and 15

(d) 4 and 12

**Answer**

B

**Question. The sum of the digits of a two digit number is 8. If 18 is added to it, the digits of the number get reversed. The number is **

(a) 53

(b) 35

(c) 62

(d) 26

**Answer**

B

**Question. How many solutions does the system of equations p + 2q = 4 and 2p + 4q – 12 = 0 have? **

(a) 0

(b) 1

(c) 2

(d) 3

**Answer**

A

**Question. If the pair of linear equations 2x + ky – 3 = 0 and 6x + 2/3 y + 7 = 0 has a unique solution, which of the following is true? **

(a) k = 2/3

(b) k ≠ 2/3

(c) k = 2/9

(d) k ≠ 2/9

**Answer**

D

**Question. If a + b = 5and 3a + 2b = 20, find 3a + b . **

(a) 25

(b) 20

(c) 15

(d) 10

**Answer**

A

**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. Three chairs and two tables cost ₹ 1850.Five chairs and three tables cost ₹ 2850. Find the total cost of one chair and one table. **

(a) ₹ 800

(b) ₹ 850

(c) ₹ 900

(d) ₹ 950

**Answer**

B

**Question. If the cost of 3 audio cassettes and 2 VCDs is ₹ 350 and that of 2 audio cassettes and 3 VCDs is ₹ 425, what is the cost of a VCD? **

(a) ₹ 140

(b) ₹ 125

(c) ₹ 115

(d) ₹ 110

**Answer**

C

**Question. A part of the monthly expenses of a family is constant and the remaining varies with the price of wheat. When the price of wheat is ` 250 per quintal, the monthly expenses of the family is ₹ 1000 and when it is ₹ 240 per quintal, the monthly expenses is ₹ 980. Find the monthly expenses of the family on wheat when the cost of wheat is ₹ 350 a quintal. **

(a) ₹ 900

(b) ₹ 350

(c) ₹ 650

(d) ₹ 700

**Answer**

D

**Question. Find the unique solution of the system of simultaneous equations 2x – y = 2 and 4x – y = 4. **

(a) x = 0,y =1

(b) x = 0,y = 0

(c) x =1,y = 0

(d) x =1,y =1

**Answer**

C

**Question. Five years ago, a father’s age was seven times his son’s age. Five years from now, the father’s age will be thrice the son’s age. What are the respective present ages of father and son? **

(a) 40 years, 10 years

(b) 10 years, 40 years

(c) 25 years, 5 years

(d) 30 years, 8 years

**Answer**

A

**Question. The side of a square is 4m more than the side of another square. The sum of their areas is 208 sq. m. What is the side of the larger square? **

(a) 12m

(b) 8m

(c) 9m

(d) 5m

**Answer**

A

**Question. If the system of equations 4x + y = 3 and (2k -1) x +(k -1)y = 2k +1 is inconsistent, then k = **

(a) 2/3

(b) -2/3

(c) -3/2

(d) 3/2

**Answer**

D

**Question. If the system of equations **

4x+3y=9

2ax+3(a+b)y=18

has infinitely many solutions, then

(a) b = 2a

(b) a = 2b

(c) a +2b = 0

(d) 2a- b = 0

**Answer**

B

**Question. The value of k for which the system of equations kx – y = 2, 6x -2y = 3 has a unique solution is **

(a) = 0

(b) = 3

(c) ¹ 0

(d) ¹ 3

**Answer**

**Question. If the system of equations 2x +3y = 7 **

(a + b)x +(2a – b)y = 21

has infinitely many solutions, then

(a) a = 1, b = 5

(b) a = –1, b = 5

(c) a = 5, b = 1

(d) a= 5, b = -1

**Answer**

C

**Question. If am¹ bl, then the system of equations **

ax + by = c, lx + my = n

(a) has a unique solution

(b) has no solution

(c) has infinitely many solutions

(d) may or may not have a solution

**Answer**

A

**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 equations x = a and y = b graphically represent lines which are **

(a) parallel

(b) intersecting at (b, a)

(c) coincident

(d) intersecting at (a, b)

**Answer**

D

**Question. A pair of linear equations in two variables cannot have **

(a) a unique solution

(b) no solution

(c) infinitely many solutions

(d) exactly two solutions

**Answer**

D

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

(a) no solution

(b) a unique solution

(c) two solutions

(d) infinitely many solutions

**Answer**

B

**Question. If x = a and y = b is the solution of the equations x + y = 5 and x – y = 7, then values of a and b are respectively **

(a) 1 and 4

(b) 6 and –1

(c) – 6 and 1

(d) –1 and –6

**Answer**

B

**Question. A pair of linear equations which has a unique solution x = -1, y = -2 is **

(a) x – y =1; 2x +3y = 5

(b) 2x -3y = 4; x -5y = 9

(c) x + y -3 = 0; x – y =1

(d) x + y +3= 0; 2x -3y +5 = 0

**Answer**

B

**Question. If the lines given by 3x +2ky = 2 and 2x +5y +1 = 0 are parallel, then the value of k is **

(a) -5/4

(b) 2/5

(c) 15/4

(d) 3/2

**Answer**

C

**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=0/4x+10y+8=0

(c) 2x-3y=0/3x+2y=0/x-4y=0

(d) x-4y=14/5x-y=13

**Answer**

B

**Question. The value of k for which the system of equation 2x +3y = 7 and 8x +(k + 4)y -28 = 0 has infinitely many solution is **

(a) –8

(b) 8

(c) 3

(d) –3

**Answer**

B

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

(a) 3 and 5

(b) 5 and 3

(c) 3 and 1

(d) –1 and –3

**Answer**

C

**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. The value of g for which the system of equations 5gx -2y =1 and 10x + y = 3 has a unique solution is **

(a) = 4

(b) ¹ 4

(c) =– 4

(d) ¹ – 4

**Answer**

D

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

(a) 2

(b) 5

(c) 5/2

(d) 3/7

**Answer**

C

**Question. The sum of the digits of a two digit number is 12. If 18 is subtracted from it, the digits of the number get reversed. The number is **

(a) 57

(b) 75

(c) 84

(d) 48

**Answer**

B

**Question. If the lines given by 3x +2ky = 2 and 2x +5y +1 = 0 are parallel, then the value of k is **

(a) 3/2

(b) 15/4

(c) 2/5

(d) – 5/4

**Answer**

B

**Question. One equation of a pair of dependent linear equations is 3x – 4 y = 7. The second equation can be **

(a) – 6x +8 y =14

(b) –6x +8 y +14 = 0

(c) 6x +8 y =14

(d) -6x -8 y -14 = 0

**Answer**

B

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

(a) always intersecting

(b) always coincident

(c) intersecting or coincident

(d) parallel

**Answer**

B

**Question. If x = a, y = b is the solution of the equation x + y = 3 and x – y = 5, then the values of a and b are, respectively **

(a) 4 and –1

(b) 1 and 2

(c) –1 and 4

(d) 2 and 3

**Answer**

C

**Question. If we add 1 to the numerator and denominator of a fraction, it becomes 1/2 . It becomes 1/3 if we only add 1 to the denominator. The fraction is **

(a) 3/4

(b) 2/5

(c) 3/5

(d) 1/4

**Answer**

C

**Question. The pair of equations x +2y -3 = 0 and 4x +5y = 8 has **

(a) no solution

(b) infinitely many solutions

(c) a unique solution

(d) exactly two solutions

**Answer**

C

**Question. The value of c for which the pair of equations 4x -5y +7 = 0 and 2cx -10 y +8 = 0 has no solution is **

(a) 8

(b) – 8

(c) 4

(d) – 4

**Answer**

A

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

(a) coincident

(b) parallel

(c) intersecting at (a, b)

(d) intersecting at (b, a)

**Answer**

C

**Question. If the lines given by 2x -5y +10 = 0 and kx +15y -30 = 0 are coincident, then the value of k is **

(a) –6

(b) 6

(c) 1/3

(d) -1/3

**Answer**

C

**Question. A pair of linear equations which has a unique solution x =1, y = -3 is **

(a) x – y = 4; 2x +3y = 5

(b) 2x – y = -5; 5x -2y =11

(c) 3x + y = 0; x +2y = -5

(d) x + y = -2; 4x +3y = 5 2

**Answer**

B

**Question. Anmol’s age is six times his son’s age. Four years hence, the age of Anmol will be four times his son’s age. The present age in years, of the father and the son are respectively **

(a) 24 and 4

(b) 30 and 5

(c) 36 and 6

(d) 24 and 3 2

**Answer**

B

**Question. The pair of equations 6x – 4 y +9 = 0 and 3x -2y +10 = 0 has **

(a) a unique solution

(b) no solution

(c) exactly two solutions

(d) infinitely many solutions

**Answer**

C

**Question. A pair of linear equations cannot have exactly two solutions. **

**Answer**

T

**Question. If two lines are parallel, then they represent a pair of inconsistent linear equations. **

**Answer**

T

**Question. State whether the following statements are true or false. Justify your answer.****(i) The pair of equations 3x – 4 y =1 and 4x +3y =1 has a unique solution.****(ii) For the pair of equations 4x +ly = –3 and 6x +9 y + 4 = 0 to have no solution, the value of l should not be **

**Answer**

(i) True (ii) True

**Question. A pair of linear equations in two variables may not have infinitely many solutions. **

**Answer**

T

**Question. The pair of equations 4x -5y = 8 and 8x -10 y = 3 has a unique solution. **

**Answer**

F

**Questin. State whether the following statements are true or false. Justify your answer.****(i) The equations x/2+y+(1/5) and 4x+8y+(8/5)=0 represent a pair of coincident lines.****(ii) For all real values of k, except –6, the pair of equations kx -3y = 5 and 2x + y = 7 has a unique solution. **

**Answer**

(i) True (ii) False

**Question. (i) For what values of a and b, will the following pair of linear equations have infinitely many solutions?****x +2y =1; (a – b)x +(a + b)y = a + b -2****(ii) Solve for x and y****x/a + y/b =a + b , x/a2 + y/b2 = 2, a, b ≠ 0 **

**Answer**

(ii) x=20 y=30 ∠A=130° ∠B=100° ∠C=50° ∠D=80°

(i) x =7 and y =9, values –1 and 30/7

**Question. (i) Draw the graphs of the equations y = 3, y = 5 and 2x – y – 4 = 0. Also, find the area of the quadrilateral formed by the lines and the y-axis.(ii) A motorboat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.**

**Answer**

(i) x =1, y = 4, Areas = 8 sq. units, 2 square units; ratio = 4 : 1

(ii) Speed of the bus is 60 km/h; Speed of the train is 90 km/h

**Question. (i) Graphically solve the pair of equations: 2x + y = 6, 2x – y +2 = 0 Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.****(ii) Saksham travels 360 km to his home partly by train and partly by bus. He takes four and a half hours if he travels 90 km by bus and the remaining by train. If he travels 120 km by bus and remaining by train, he takes 10 minutes longer. Find the speed of the train and the bus separately.**

**Answer**

(i) Area of trapezium=8 sq. units

(ii) Speed of the boat in still water = 10 km/h; Speed of the stream = 4 km/h

**Question. A linear equation in two variables always has infinitely many solutions. **

**Answer**

T

**Question. A pair of linear equations in two variables is said to be consistent if it has no solution. **

**Answer**

F

**Question. (i) If 2x + y = 23 and 4x – y =19, find the values of 3y – 4x and y/x+3.****(ii) The angles of a cyclic quadrilateral ABCD are ∠A = (6x +10)°, ∠B =(5x)°, ∠C = (x + y)°, ∠D = (3y -10)° Find x and y, and hence the value of the four angles.**

**Answer**

(i) a= 3, b=1(ii) x= a2 , y= b2

**Question. A pair of intersecting lines represent a pair of linear equations in two variables having a unique solution. **

**Answer**

T

**Question. An equation of the form ax + by + c = 0, where a, b and c are real numbers is called a linear equation in two variables. **

**Answer**

F

**Question. For the pair of equations lx +3y = -7, 2x -6 y =14 to have infinitely many solutions, the value of λ should be 1. Is the statement true? Give reason.**

**Answer**

False, it should be –1

**Question. How many solutions does the pair of equations. ****x +2y = 3 and 1/2 x + y 3/2 – = 0 have?**

**Answer**

Infinite

**Question. Is the pair of equations x – y = 5 and 2y – x =10 inconsistent? Justify your answer.**

**Answer**

No, since a1/a2≠b1/b2 , so it has a unique solution

**Question. Is the pair of equations 3x -5y = 6 and 4x -6 y = 7 consistent? Justify your answer.**

**Answer**

Yes, since a1/a2≠b1/b2

**Question. Is it true to say that the pair of equations -2x + y +3 = 0 and 1/3 x +2y -1 = 0 has a unique solution? **

**Answer**

Yes, a_{1}/a_{2}≠b_{1}/b_{2}

**Question. Write the number of solutions of the following pair of linear equations: ****3x -7y =1 and 6x -14 y -3 = 0**

**Answer**

0

**Question. Do the equations 5x +7y = 8 and 10x +14 y = 4 represent a pair of coincident lines? Justify your answer.**

**Answer**

No, because a_{1}/a_{2}≠b_{1}/b_{2} ≠c_{1}/c_{2} ¹ , so the equations represent parallel lines.

Our teachers have developed really good **Multiple Choice Questions** covering all important topics in each chapter which are expected to come in upcoming tests and exams, as MCQs are coming in all exams now therefore practice them carefully to get full understanding of topics and get good marks. Download the latest questions with multiple choice answers for Class 10 Linear Equations in pdf or read online for free.

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