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cbse 10th Standard Maths Pair of Linear Equation in Two Variables Important Questions And Answers Study Material - QB365 Set A

Published on: 22/10/2025

Question Set A

cbse 10th Standard Maths Pair of Linear Equation in Two Variables Important Questions And Answers Study Material - QB365

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Std: 10th Standard CBSE - Maths

chapter: Pair of Linear Equation in Two Variables - Important Questions And Answers

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Questions:

Multiple Choice Question

40 x 1 = 40

The ratio of a two-digit number and the sum of its digits is 7:1. How many such two-digit numbers are possible?com

(a)

(b)

(c)

(d)

infinitely many

The solution of the pair of equations x+y=a+b and a x-b y=a²-b² is

(a)

x=b, y=a

(b)

x=a, y=b

(c)

x=-a, y=b

(d)

x=a, y=-b

Two lines are given to be parallel. The equation of one of the lines is 3x - 2y = 5. The equation of the second line can be

(a)

9x + 8y = 7

(b)

-12x - 8y = 7

(c)

-12x + 8y = 7

(d)

12x + 8y = 7

The pair of equations ax + 2y = 9 and 3x - by = 18 represent parallel lines, where a, b are integers, if

(a)

a=b

(b)

3a = 2b

(c)

2a = 3b

(d)

ab = 6

The given pair of linear equations is non-intersecting. Which of the following statement is true?

(a)

\(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)

(b)

\(\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)

(c)

\(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}=\frac{c_1}{c_2}\)

(d)

\(\frac{a_1}{a_2} \neq \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)

The lines represented by linear equations x = a and y= b\((a \neq b)\)are

(a)

intersecting at (a,b)

(b)

intersecting at (b, a)

(c)

parallel

(d)

coincident

The pair of equations 3^x+y =81. 81^x-y = 3 has

(a)

no solution

(b)

unique solution

(c)

infinitelymany solutions

(d)

\(x=2 \frac{1}{8}, y=1 \frac{7}{8}\)

The pair of equations y = 0 and y = - 7 has

(a)

one solution

(b)

two solutions

(c)

infinitelymany solutions

(d)

no solution

Which of the following pair of equations are inconsistent?

(a)

3x - y = 9, x - \(\frac{y}{3}\)=3

(b)

4x.+ 3y = 24, - 2x+ 3y = 6

(c)

5x - y = 10,10x-2y = 20

(d)

2x+ y=3,-4x+2y=10

10.

A fraction becomes 4/5 when 1 is added to each of the numerator and denominator. However, if..we subtract 5 from each of them, it becomes 1/2. Then, numerator of the fraction is

(a)

(b)

(c)

(d)

11.

The values of x and y which satisfy the equations: 47x + 31y = 63 and 31x + 47y=15 are ____________

(a)

2 and -1

(b)

-2 and 1

(c)

-2 and -1

(d)

2 and 1

12.

Solution for ax + by = a – b and bx – ay = a + b is

(a)

1, -1

(b)

-a, -b

(c)

a, b

(d)

-1, 1

13.

Find the point on Cartesian plane where the line 3x – 2y = 6 intersects the y axis

(a)

(3, 2)

(b)

(-1, -2)

(c)

(0, -3)

(d)

(1, 2)

14.

The graph below represents equations that have

(a)

unique solution

(b)

solution as 0

(c)

infinite solution

(d)

no solution

15.

Find the solution to the following system of linear equations:
\(\sqrt { 5 } x+\sqrt { 3 } y=8\\ \sqrt { 5 } x-\sqrt { 3 } y=2\)

(a)

(\(\sqrt { 5 } \),-\(\sqrt { 3 } \))

(b)

(\(\sqrt { 3 } \),-\(\sqrt { 5 } \))

(c)

(\(\sqrt { 5 } \),\(\sqrt { 3 } \))

(d)

(\(\sqrt { 3 } \),\(\sqrt { 5 } \))

16.

The pair of equations y = 0 and y = -7 has :

(a)

one solution

(b)

infinitely many solutions

(c)

no solution

(d)

two solutions

17.

The difference between two numbers is 45 and one number is six times the other. Find them

(a)

7,42

(b)

8,48

(c)

6,36

(d)

9,54

18.

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 – 14x + 4 = 0

(c)

10x – 14y = -4

(d)

10x + 14y + 4 =0

19.

The sum of ages of A and B is 50 years. A said to B, “I am twice as old as you were when I was as old as you are. Find the present age of B

(a)

(b)

(c)

(d)

20.

Adding 1 to the numerator and subtracting 1 from the denominator of a fraction makes it 1. However, if 1 is added only to the denominator of the fraction it becomes ½ . The fraction is______

(a)

2/3

(b)

3/5

(c)

5/3

(d)

3/2

21.

The value of x, y in the following
2^x+2 – 3^y+1 = 5 ………(1)
2^x + 3^y = 17 ………(2)

(a)

3,2

(b)

2,-3

(c)

-2,3

(d)

2,3

22.

The number of solutions of equations represented by this graph is

(a)

Infinite

(b)

(c)

(d)

No solution

23.

What is the solution of the equations \(\sqrt { 2 } x-\sqrt { 3 } y\ =\ 0\ and\ \sqrt { 5 } x+\sqrt { 2 } y=0\)

(a)

0, 2

(b)

2, 0

(c)

0, 0

(d)

None

24.

The value of x in the system x – 3y = 7; 3x – 3y = 15 is

(a)

x = – 11

(b)

x = – 4

(c)

x = 11

(d)

x = 4

25.

The values of ‘a’ and ‘b’ for which (2a – 1)x – 3y = 5, 3x + (b – 2)y = 3, has infinitely many solution are

(a)

a=3, b= \(\frac { 1 }{ 5 } \)

(b)

a=3, b =\(\frac { 2 }{ 7 } \)

(c)

\(a=\frac { 7 }{ 2 } ,b=\frac { 1 }{ 5 } \)

(d)

\(a=\frac { 1 }{ 5 } \),b= 3

26.

The pair of linerar equations 2x+ky-3, 6x+ \(\frac { 2 }{ 3 } \)y+7 =0 have a unique solution for all values of k except

(a)

\(k\neq \frac { 2 }{ 3 } \)

(b)

\(k=\frac { 2 }{ 3 } \)

(c)

\(k\neq \frac { 2 }{ 9 } \)

(d)

\(k=\frac { 2 }{ 9 } \)

27.

The value of x, y in the following pair of Linear equations is
\(\frac { a }{ x } -\frac { b }{ x } =0\) ... (1)
\(\frac { { ab }^{ 2 } }{ x } +\frac { { a }^{ 2 }b }{ y } ={ a }^{ 2 }+b^{ 2 }\)..... (2)

(a)

b, a

(b)

a, b

(c)

a,-b

(d)

-a,b

28.

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

(a)

(b)

No solution

(c)

Infinite

(d)

29.

Find the value of ‘a” for which the system of equations 3x + 2y – 4 = 0 and ax – y – 3 = 0, will represent intersecting lines

(a)

a = 3/2

(b)

a ≠ 2/3

(c)

a = 2/3

(d)

a ≠ 3/2

30.

The number of solutions of the pair of linear equations x + 2y – 8 = 0 and 2x + 4y = 16 are

(a)

Infinitely many

(b)

(c)

(d)

None

31.

If two lines are parallel to each other the system of equation is

(a)

Consistent dependent

(b)

Inconsistent

(c)

Inconsistent dependent

(d)

consistent

32.

Find the solution to the following system of linear equations
0.2x + 0.3y = 1.2
0.1x – 0.1y = 0.1

(a)

(2,1)

(b)

(2,3)

(c)

(1,2)

(d)

(3,2)

33.

If the pair of equation has no solution, then the pair of equation is

(a)

inconsistent

(b)

none of these

(c)

coincident

(d)

consistent

34.

If x=a, y=b is the solution of the pair of equation x-y=2 and x+y=4 then what will be value of a and b

(a)

2,1

(b)

3,1

(c)

4,6

(d)

1,2

35.

What will be the solution of these equations ax+by=a-b, bx-ay=a+b

(a)

x=1, y=2

(b)

x=2,y=-1

(c)

x=-2, y=-2

(d)

x=1, y=-1

36.

Five years ago, A was thrice as old as B and ten years later, A shall be twice as old as B. What is the present age of A.

(a)

(b)

(c)

(d)

37.

A fraction becomes when subtracted from the numerator and it becomes . when 8 is added to its denominator. Find the fraction

(a)

4/12

(b)

3/13

(c)

5/12

(d)

11/7

38.

The sum of two digits and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number

(a)

(b)

(c)

(d)

39.

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

40.

Customers are asked to stand in the lines. If one customer is extra in a line, then there would be two less lines. If one customer is less in line, there would be three more lines. Find the number of students in the class

(a)

(b)

(c)

(d)