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## NCERT Solution For Class 10 Maths Chapter 3## Pair of Linear Equations in Two VariablesNCERT Solution For Class 10 Maths Chapter 3 Complete Solution
3.1 Introduction
3.2 Pair Of Linear Equations In Two Variables 3.3 Graphical Method Of Solution Of A Pair Of Linear Equations 3.4 Algebraic Methods Of Solving A Pair Of Linear Equations 3.4.1 Substitution Method 3.4.2 Elimination Method 3.4.3 Cross-Multiplication Method 3.5 Equations Reducible To A Pair Of Linear Equations In Two Variables 3.6 Summary Exercise 3.11. Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be." (Isn't this interesting?) Represent this situation algebraically and graphically. AnswerxAnd, present age of daughter is represented by yThen Seven years ago, Age of Aftab = x -7Age of daughter = y-7According to the question, ( x - 7) = 7 (y – 7 )x – 7 = 7 y – 49x- 7y = - 49 + 7 x – 7y = - 42 …(i)x = 7y – 42 Putting y = 5, 6 and 7, we getx = 7 × 5 - 42 = 35 - 42 = - 7x = 7 × 6 - 42 = 42 – 42 = 0x = 7 × 7 – 42 = 49 – 42 = 7
Three years from now , Age of Aftab = x +3Age of daughter = y +3According to the question, ( x + 3) = 3 (y + 3)x + 3 = 3y + 9x -3y = 9-3x -3y = 6 …(ii)x = 3y + 6 Putting, y = -2,-1 and 0, we getx = 3 × - 2 + 6 = -6 + 6 =0x = 3 × - 1 + 6 = -3 + 6 = 3x = 3 × 0 + 6 = 0 + 6 = 6
Algebraic representation From equation (i) and (ii)x – 7y = – 42 …(i)x - 3y = 6 …(ii)Graphical representation 2. 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 and geometrically. AnswerLet cost of one bat = Rs xCost of one ball = Rs y3 bats and 6 balls for Rs 3900 So that 3 x + 6y = 3900 … (i)Dividing equation by 3, we get x + 2y = 1300 Subtracting 2 y both side we getx = 1300 – 2y Putting y = -1300, 0 and 1300 we getx = 1300 – 2 (-1300) = 1300 + 2600 = 3900x = 1300 -2(0) = 1300 - 0 = 1300x = 1300 – 2(1300) = 1300 – 2600 = - 1300
Given that she buys another bat and 2 more balls of the same kind for Rs 1300 So, we get x + 2y = 1300 … (ii)Subtracting 2y both side we get x = 1300 – 2yPutting y = - 1300, 0 and 1300 we getx = 1300 – 2 (-1300) = 1300 + 2600 = 3900x = 1300 – 2 (0) = 1300 - 0 = 1300x = 1300 – 2(1300) = 1300 – 2600 = -1300
Algebraic representation 3 x + 6y = 3900 … (i)x + 2y = 1300 … (ii)Graphical representation, 3. The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically. AnswerLet cost each kg of apples = Rs xCost of each kg of grapes = Rs yGiven that the cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160 So that 2 x + y = 160 … (i)2 x = 160 - yx = (160 – y)/2Let y = 0 , 80 and 160, we getx = (160 – ( 0 )/2 = 80x = (160- 80 )/2 = 40x = (160 – 2 × 80)/2 = 0
Given that the cost of 4 kg of apples and 2 kg of grapes is Rs 300 So we get 4 x + 2y = 300 … (ii)Dividing by 2 we get 2 x + y = 150Subtracting 2 x both side, we gety = 150 – 2xPutting x = 0 , 50 , 100 we gety = 150 – 2 × 0 = 150y = 150 – 2 × 50 = 50y = 150 – 2 × (100) = -50
Algebraic representation, 2 x + y = 160 … (i)4 x + 2y = 300 … (ii)Graphical representation,For Getting Complet Solution Please Visit Our Official Website:- https://sscchslinfo.in/
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