Exercise 3.3 (NCERT) – Pair of Linear Equations in Two Variables, Class 10
| Chapter 3 | Exercise 3.3 | Class 10 |
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Below are the solutions of every question of exercise 3.3 of chapter 3, Pair of Linear Equations in Two Variables, NCERT of class 10. YouTube video tutorial of every question is also embedded along with the written solution.
Question 1
Solve the following pair of linear equations by the elimination method and the substitution method.
(i) x + y = 5 and 2x – 3y = 4
Elimination Method
Substitution Method
Answer: x = 19/5, y = 6/5
(ii) 3x + 4y = 10 and 2x – 2y = 2
Elimination Method
Substitution Method
Answer: x = 2, y = 1
(iii) 3x – 5y – 4 = 0 and 9x = 2y + 7
Elimination Method
Substitution Method
Answer: x = 9/13, y = -5/13
(iv) x/2 + 2y/3 = -1
x – y/3 = 3
Elimination Method
Substitution Method
Answer: x = 2, y = 3
Question 2
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 1/2 if we only add 1 to the denominator. What is the fraction?
Condition 1
Condition 2
Subtract (i) from (ii) to eliminate y
Substitute in (i)
Answer: 3/5
(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?
Let Nuri’s age = x
& Sonu’s age = y
Condition 1: 5 Years ago
Condition 2: 10 Years later
Subtract (ii) from (i) to eliminate x
Substitute in (ii)
Answer: Nuri’s Age = x = 50 Years, Sonu’s Age = y = 20 Years
(iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
Let tens digit x
units digit y
Number = 10x + y
Reversed Number = 10y + x
Condition 1
Sum of digits = 0
=> x + y = 9 … (i)
Condition 2
9 times number = 2 times number obtained by reversing the digits
Add (1) and (2) to eliminate y
Substitute x in 1
The number is : 18
Answer: 18
(iv) Meena went to a bank to withdraw Rs. 2000. She asked the cashier to give her Rs. 50 and Rs. 100 notes only. Meena got 25 notes in all. Find how many notes of Rs. 50 and Rs. 100 she received.
Let ₹50 notes = x
& Let ₹100 notes = y
Condition 1
Total notes = 25
Condition 1
Total money = 2000
Subtract (1) and (2) to eliminate x
Substitute y in 1
Answer: Rs. 50 Notes = 10, Rs. 100 Notes = 15
(v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs. 27 for a book kept for seven days, while Susy paid Rs. 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Let fixed charge = x
Extra charge/day = y
Condition 1
Saritha paid Rs. 27 for 7 days
Condition 2
Susy paid Rs. 21 for 5 days
Subtract (2) and (1) to eliminate x
Substitute y in (ii)
Answer: Fixed Charges = x = Rs. 15, Additional Per Day Charge = Rs. 3