CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set 04

Question. Solve: 99𝑥 + 101𝑦 = 499: 101𝑥 + 99𝑦 = 501
Answer : Add two given equations
𝑥+𝑦 = 5 (1)
𝑆𝑢𝑏𝑡𝑟𝑎𝑐𝑡 𝑡𝑤𝑜 𝑔𝑖𝑣𝑒𝑛 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛𝑠
𝑥– 𝑦 = 1 (2)
(1) + (2)
2𝑥 = 6
𝑥 = 3
𝑆𝑢𝑏 𝑥 =3 𝑖𝑛 (1) 𝑦 = 2

Question. Anu’s father is three times as old as Anu. After five years, his age will be two and half times as old as Anu. Represent this situation algebraically only.
Answer : 
𝐿𝑒𝑡 𝐴𝑛𝑢’𝑠 𝑎𝑔𝑒 = 𝑥
𝐹𝑎𝑡ℎ𝑒𝑟’𝑠 𝑎𝑔𝑒 = 𝑦
𝑥 = 3𝑦
𝑦+5 =(2X1/2 )( 𝑥+5)
2𝑦 + 10 = 5𝑥+25
5𝑥 – 2𝑦 = 15

Question. Solve the pair of linear equations by elemination method:
i. 𝑥 – 𝑦 + 1 = 0
ii. 4𝑥 + 3𝑦 – 10 = 0
Answer : 
(2) × 4 →
4x – 4y + 4 = 0
4x + y – 6 = 0
5y – 10 = 0
y = 2
x = 1

Question. Four chairs and three tables cost 2100/- and 5 chairs and 2 tables cost 1750/-. Find the cost of a chair and table respectively
Answer : Let the cost of 1 chair be x /- and that of table be y/-
Then by given condition,
4x + 3y = 2100 ……………..(i)
5x + 2y = 1750 …………..(ii)
Solving x = 150/- and y = 500/-
Cost of one chair = 150 /- and cost of 1 table = 500/-

Question. Determine the values of a and b for which the following system of linear equations have infinite solutions
2𝑥 − (𝑎 − 4)𝑦 = 2𝑏 + 1 ;
4𝑥 − (𝑎 − 1) 𝑦 = 5𝑏 − 1
Answer : A pair of linear equation has infinitely many solutions, if a₁/a₂ = b₁/b₂ = c₁/c₂
Therefore 2/4 = − a − 4/ − (a − 1) = 2b + 1/5b − 1
Solving, a = 7 and b = 3

Question. Solve by elimination:
a. 𝑥 − 𝑦 + 1 = 0 𝑎𝑛𝑑 4𝑥 + 3𝑦 − 10 = 0
b. 3𝑥 − 4𝑦 = 15 𝑎𝑛𝑑 2𝑥 – 2𝑦 = 8
Answer : (i) x = 1, y = 2
(ii) x = 1, y = -3

Question. Yash scored 40 marks in a test, receiving 3 marks for each correct answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each wrong answer, then Yash would have scored 50 marks. How many questions were there in the test?
Answer : Let right answer questions attempt by Yash be x wrong answer questions be y
Then, 3x – y = 40………….(i)
4x - 2y = 50 …………(ii)
Solving we get x = 15, y = 5
Total number of questions in the test = x + y = 15 + 5 = 20

Question. The age of the father is twice the sum of the ages of his 2 children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father
Answer : Let the present ages of children be x years and y years respectively.
Present age of father is twice the sum of ages of his 2 children = 2(x + y) ………..(i)
Then by question,
(x + 20) + (y + 20) = 2(x + y) + 20
x + y + 40 = 2x + 2y + 20
x + y = 20
Putting (x + y) in (i),
2(x + y) = 2 × 20 = 40