CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set E

Fill in the Blanks

DIRECTIONS : Complete the following statements with an appropriate word / term to be filled in the blank space(s).

Question. If the lines intersect at a point, then that point gives the unique solution of the two equations. In this case, the pair of equations is .................
Answer : consistent

Question. If the lines are parallel, then the pair of equations has no solution. In this case, the pair of equations is ..............
Answer : inconsistent.

Question. Two distinct natural numbers are such that the sum of one number and twice the other number is 6. The two numbers are ..............
Answer : 4 and 1

Question. If p + q = k, p – q = n and k > n, then q is ................... (positive/negative).
Answer : positive

Question. Sum of the ages of X and Y, 12 years, ago, was 48 years and sum of the ages of X and Y, 12 years hence will be 96 years. Present age of X is ..............
Answer : Cannot be determined

Question. The number of common solutions for the system of linear equations 5x + 4y + 6 = 0 and 10x + 8y = 12 is .............
Answer : zero

Question. If 2x + 3y = 5 and 3x + 2y = 10, then x – y = ............... .
Answer : 5

Question. If 1/x + 1/y = k and 1/x – 1/y = k, then the value of y is ...........
Answer : Does not exist

True / False

DIRECTIONS : Read the following statements and write your answer as true or false.

Question. If a pair of linear equations is given by a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 and a₁/a₂ ≠ b₁/b₂. In this case, the pair of linear equations is consistent.
Answer : True

Question. If a pair of linear equations is given by a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 and a₁/a₂ = b₁/b₂ ≠ c₁/c₂. In this case, the pair of linear equations is consistent.
Answer : False

Question. If a pair of linear equations is given by a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 and a₁/a₂ = b₁/b₂ = c₁/c₂. In this case, the pair of linear equations is consistent.
Answer : True

Question. 3x – y = 3, 9x – 3y = 9 has infinite solution.
Answer : True

Question. √2x + √3y = 0 , √​​​​​​​3x − √8y = 0 has no solution.
Answer : False

Question. 3x + 2y = 5, 2x – 3y = 7 are consistent pair of equation.
Answer : True

Question. In a Δ ABC, ∠C = 3 ∠B = 2 (∠ A + ∠ B), then angles are 20°, 40°, 100°.
Answer : False

CASE STUDY 1:

An alumni association is an association of former students. These associations often organize social events, publish newsletters or magazines and raise funds for the organisation.The alumni meet of two batches of a college- batch A & batch B were held on the same day in the same hotel in two separate halls “Rose” and “Jasmine”. The rents were the same for both the halls. The expense for each hall is equal to the fixed rent of each hall and proportional to the number of persons attending each meet. 50 persons attended the meet in “Rose” hall, and the organisers had to pay ₹ 10000 towards the hotel charges. 25 guests attended the meet in “Jasmine” hall and the organisers had to pay ₹ 7500 towards the hotel charges. Denote the fixed rent by ₹ x and proportional expense per person by ₹ y.

Question. Represent algebraically the situation in hall “Rose”.
a) 50𝑥+𝑦=10000
b) 50𝑥−𝑦=10000
c) 𝑥+50𝑦=10000
d) 𝑥−50𝑦=10000
Answer : C

Question. Represent algebraically the situation in hall “Jasmine”
a) 𝑥+25𝑦=7500
b) 𝑥−25𝑦=7500
c) 25𝑥+𝑦=7500
d) 25𝑥−𝑦=7500
Answer : A

Question. What is the fixed rent of the halls?
a) ₹2500
b) ₹3300
c) ₹ 4000
d) ₹5000
Answer : D

Question. Find the amount the hotel charged per person.
a) ₹ 150
b) ₹ 190
c) ₹130
d) ₹ 100
Answer : D

Very Short Answer type Questions

Question. Find the value of (𝑥 + 𝑦)𝑖𝑓 ,3𝑥 − 2𝑦 = 5 𝑎𝑛𝑑 3𝑦 − 2𝑥 = 3
Answer : x + y = 8

Question. Solve for 𝑥 𝑎𝑛𝑑 𝑦 : 99𝑥 + 101 𝑦 = 499,101𝑥 + 99 𝑦 = 501
Answer : intersecting

Question. How many solutions do the equations 𝑦 = 0,𝑦 = − 7 posses?
Answer : X + y = 3, x – y =1

Question. Do the equations 𝑦 = 𝑥 𝑎𝑛𝑑 𝑦 = 𝑥 + 3 represent parallel lines?
Answer : Yes

Question. The value of k for which the equations 𝑘𝑥 + 𝑦 = 6 𝑎𝑛𝑑 6𝑥 + 2𝑦 = 12 will have infinitely many solutions is
Answer : y = 11− 3𝑋 / 5

Question. Express ‘x’ in terms of y of the equation 3x-y = 2 also check whether (-1,3) satisfies the equation or not?
Answer : 9 & 6

Question. The sum of the digits of a two-digit number is 9. If 27 is added to it the number gets reversed. The number is
Answer : K = 2

Question. In how many points do the lines represented by the equations 𝑥 − 𝑦 = 0 𝑎𝑛𝑑 𝑥 + 𝑦 = 0 intersect?
Answer : one

Question. If 𝑥 = 𝑎 ,𝑦 = 𝑏 is the solutions of the equations 𝑥 − 𝑦 = 2 𝑎𝑛𝑑 𝑥 + 𝑦 = 4 find a &b.
Answer : 36

Question. Find whether the lines representing the following pair of linear equations are intersecting, parallel or coinciding. 2𝑥 − 3𝑦 + 6 = 0; 4𝑥 − 5𝑦 + 2 = 0
Answer : K = 3

Short Answer type Questions

Please click on below link to download CBSE Class 10 Mathematics Pair of Linear Equation In Two Variables Worksheet Set E