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CBSE - Class 10 Mathematics Pair of linear equations in two variable Worksheet

1.
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
2.

If the sum of first 7 terms of an A.P. is 49 and that of first 17 terms is 289, find the sum of n terms.

A)

n^2

 B)

n^3

 C)

n/2

 D)

2n
3.
Indicate the pair or pairs representing simultaneous linear equations (solvable). 7x – 3y = 5 & 2x + 5y = 1
4.
Choose the correct option: For a pair to be consistent and dependent the pair must have ________.
A) No solution B) Unique solution C) Infinitely many solutions D) None of these
5.
Solve the following pair of linear equations by the substitution method. (iv) 0.2x + 0.3y = 1.3; 0.4x + 0.5y = 2.3
6.

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

A)

One solution

 B)

Two solutions

 C)

Infinitely many solutions

 D)

No solution
7.
Choose the correct option: Example of linear equation involving two variables is _________.
A) 7x + 3y + 4z = 20 B) 6x + 2y = 10 C) 8x = 2+10 D) 7a + 8b + 9c = 10 + 5
8.

Two women and 5 men can together finish a piece of embroidery in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman to finish the embroidery, and time taken by 1 man alone

A)

6 and 8 days

 B)

36 and 18 days

 C)

18 and 18 days

 D)

32 and 6 days
9.

One equation of a pair of dependent linear equations is 2x + 5y = 3. The second equation will be

A)

2x + 5y = 6

 B)

3x + 5y = 3

 C)

-10x – 25y + 15 = 0

 D)

10x + 25y = 15
10.

 For what value of k, are the numbers x, (2x + k) and (3x + 6) three consecutive terms of an A.P

A)

k=3

 B)

k=4

 C)

k=5

 D)

k=6
11.

A system of simultaneous linear eqn is said to be consistent, if it has

A)

atleast one solution

 B)

no solution
12.
Choose the correct option: For 2x + 3y = 4, y can be written in terms of x as ______.
A) y = 4 + 2x/3 B) y = 4 - 3x/2 C) x = 4 - 3y/2 D) y = 4 - 2x/3
13.

the sum of the digits of a two digit number is 15. the number obtained by interchanging the digit exceeds the given number by 9. the number is

A)

96

 B)

69

 C)

87

 D)

78
14.
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes $\frac{1}{2}$ if we only add 1 to the denominator. What is the fraction?
15.
Choose the correct option: A pair of linear equations which has a unique solution x = 2, y = –3 is _________.
A) x + y = –1, 2x - 3y = -5 B) 2x + 5y = –11, 4x+10y=-22 C) 2x – y = 1, 3x + 2y = 0 D) x – 4y –14 = 0, 5x - y -13 = 0
16.

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
17.

The larger of two supplementary angles exceeds thrice the smaller by 20 degrees. Find the angles

A)

140,40

 B)

130,50

 C)

120,60

 D)

100,80
18.
Choose the correct option: On representing x = a and y = b graphically we get ______.
A) Parallel line B) Coincident lines C) Intersecting lines at (a,b) D) Intersecting lines at (b,a)
19.
Solve the following pair of linear equations by the substitution method. (v) $\sqrt{2}x + \sqrt{3}y = 0$; $\sqrt{3}x - \sqrt{8}y = 0$
20.
Form the pair of linear equations for the following problems and find their solution by substitution method. (ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

CBSE - Class 10 Mathematics Pair of linear equations in two variable Worksheet

Answers

2.
Option A

3.
7/2 ? -3/5, so the two equations represent simultaneous equations; in this case they have only one solution.
4.
Option C
6.
Option D
7.
Option B
8.
Option B
9.
Option C
10.
Option A
11.
Option A
12.
Option D
13.
Option D
15.
Option D
16.
Option D
17.
Option A
18.
Option C
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