CBSE Class 10 Mathematics Linear Equations Assignment Set 01

CBSE Class 10 Mathematics Linear Equations Assignment Set A. Students are advised to refer to the attached assignments and practise them regularly. This will help them to identify their weak areas and will help them to score better in examination. Parents should download and give the assignments to their children for practice.

LEVEL-1

Question. Which of the following pairs of linear equations are consistent/inconsistent?
(i) x + y = 5, 2x + 2y = 10
Answer : (i) x + y = 5; 2x + 2y = 10
a₁/a₂ = 1/2
b₁/b₂ = 1/2 and
c₁/c₂ = 5/10 = 1/2
Hence, a₁/a₂ = b₁/b₂ = c₁/c₂
Therefore, these linear equations are coincident pair of lines and thus have infinite number of possible solutions. Hence, the pair of linear equations is consistent.

Question. The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 3 more balls of the same kind for Rs 1300. Represent this situation algebraically.
Answer : Let cost of one bat = Rs x
Cost of one ball = Rs y
3 bats and 6 balls for Rs 3900 So that
3x + 6y = 3900
Given that she buys another bat and 2 more balls of the same kind for Rs 1300
So, we get
x + 2y = 1300

Question. Find the number of solutions of the following pair of linear equations:
x + 2y -8=0,2x+ 4y=16
Answer : a₁/a₂ =1/2
b₁/b₂=1/2
c₁/c₂=1/2
Here a₁/a₂ = b₁/b₂= c₁/c₂
Therefore, the equations have infinite number of solutions.

Question. Two lines are given to be parallel. The equation of one of the lines is 4x+ 3y=14. Find the equation of the second line.
Solution: 8x+6y=28

LEVEL-2 ( 2 MARKS EACH)

Question. Solve the following pair of linear equations by the substitution method.
x + y = 14 ; x – y = 4
Answer : x + y = 14 ... (i)
x – y = 4 ... (ii)
From equation (i), we get
x = 14 - y ... (iii)
Putting this value in equation (ii), we get
(14 - y) - y = 4
14 - 2y = 4
10 = 2y
y = 5 ... (iv)
Putting this in equation (iii), we get
x = 9
∴ x = 9 and y = 5

Question. For which value of k will the following pair of linear equations have no solution?
3x + y = 1 (2k –1)x + (k –1)y = 2k + 1
Answer : 3x + y -1 = 0
(2k –1)x + (k –1)y - (2k + 1) = 0
a1/a2 = 3/2k-1
b1/b2 = 1/k-1 and
c1/c2 = -1/-2k-1 = 1/2k+1
For no solutions,
a1/a2 = b1/b2 ≠ c1/c2
3/2k-1 = 1/k-1 ≠ 1/2k+1
3/2k-1 = 1/k-1
3k - 3 = 2k - 1
k = 2
Hence, for k = 2, the given equation has no solution.

Assertion and Reason Based MCQ

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
(A) Both A and R are true and R is the correct explanation of A
(B) Both A and R are true but R is the NOT the correct explanation of A
(C) A is true but R is false
(D) A is false and R is True

Question. Assertion (A): If 4 chairs and 3 tables cost ₹2100 and 5 chairs and 2 tables cost ₹1750 , then the cost of 1 chair is ₹150.
Reason (R): Sum of the ages of a father and the son is 40 years. If father’s age is 3 times that of his son, then the son’s age is 12 years.
Answer : C

Question. Assertion (A): If the pair of linear equations 3x+y=3 and 6x+ky =8 does not have a solution, then the value of k=2.
Reason (R): If the pair of linear equations x+y-4=0 and 2x+ky =3 does not have a solution, then the value of k=2.
Answer : B

Question. Assertion (A): If the equation 3x-y+8=0 and 6x-ky =-16 represents coincident lines, then the value of k=2.
Reason (R): If the lines given by 3x+2ky=2 and 2x+5y+1 =0 are parallel, then the value of k=12.
Answer : C

Question. Assertion (A): For all real values of c, the pair of equation x-2y=8 and 5x-10y=c have a unique solution.
Reason (R): Two lines are given to be parallel. The equation of one of the lines is 4x+3y=14, 12x+9y=5
Answer : D

Question. Assertion (A): The solution of the pair of linear equations x+y=5 and 2x-3y =4 is x=195 and y=65
Reason (R): The solution of the pair of linear equations 3x+4y=10 and 2x-2y=2 is x=2 and y=1.
Answer : B

Please click the link below to download CBSE Class 10 Mathematics Linear Equations Assignment Set A