3x-y=0 then 4x+y/x+7y equal to
Answers
Answer:Let the present age of Aftab = x And, present age of his daughter is represented as = y Seven years ago, Aftab’s age = x – 7 Age of Aftab’s daughter = y – 7 According to the question, (x – 7) = 7 (y – 7 ) x – 7 = 7 y – 49 x – 7y = – 49 + 7 x – 7y = – 42 … (i) x = 7y – 42 Putting y = 5, 6 and 7, we get x = 7 × 5 – 42 = 35 – 42 = – 7 x = 7 × 6 – 42 = 42 – 42 = 0 x = 7 × 7 – 42 = 49 – 42 = 7
Three years from now, Aftab’s age = x + 3 Age of Aftab’s daughter = y + 3 According to the question, (x + 3) = 3 (y + 3) x + 3 = 3y + 9 x – 3y = 9 – 3 x – 3y = 6 … (ii) x = 3y + 6 Putting, y = – 2, –1 and 0, we get x = 3 × – 2 + 6 = – 6 + 6 =0 x = 3 × – 1 + 6 = – 3 + 6 = 3 x = 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.
Ans. Let cost of one bat be = Rs x And, cost of one ball be = Rs y 3 bats and 6 balls are for Rs 3900 Therefore, 3x + 6y = 3900 … (i) Dividing equation by 3, we get x + 2y = 1300 Subtracting 2y from both side we get x = 1300 – 2y Putting y = –1300, 0 and 1300 we get x = 1300 – 2 (–1300) = 1300 + 2600 = 3900 x = 1300 – 2(0) = 1300 – 0 = 1300 x = 1300 – 2(1300) = 1300 – 2600 = – 1300
Given that she buys another bat and 2 more balls of the same kind for Rs 1300
We get x + 2y = 1300 … (ii) Subtracting 2y from both sides we get x = 1300 – 2y Putting y = – 1300, 0 and 1300 we get x = 1300 – 2 (–1300) = 1300 + 2600 = 3900 x = 1300 – 2 (0) = 1300 – 0 = 1300 x = 1300 – 2(1300) = 1300 – 2600 = – 1300
Algebraic representation 3x + 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.
Ans. Let each kg of apples cost = Rs x And, cost of each kg of grapes = Rs y Given that the cost of 2 kg of apples and 1kg of grapes on a day was found to be = Rs 160 Therefore, 2 x + y = 160 … (i) 2x = 160 – y x = (160 – y)/2 Let y = 0 , 80 and 160, we get x = (160 – ( 0 )/2 = 80 x = (160– 80 )/2 = 40 x = (160 – 2 × 80)/2 = 0
Given that the cost of 4 kg of apples and 2 kg of grapes is Rs 300 Therefore, 4x + 2y = 300 … (ii) Dividing by 2 we get 2x + y = 150 Subtracting 2x from both the sides, we get y = 150 – 2x Putting x = 0 , 50 , 100 we get y = 150 – 2 × 0 = 150 y = 150 – 2 × 50 = 50 y = 150 – 2 × (100) = – 50
Algebraic representation, 2x + y = 160 … (i) 4x + 2y = 300 … (ii) Graphical representation,
Exercise 3.2
1. Form the pair of linear equations in the following problems, and find their solutions graphically.
(i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
Ans. Let the number of boys be = x Let the number of girls be = y Given that total number of students is 10 Therefore x + y = 10 Subtracting y from both the sides we get x = 10 – y Putting y = 0, 5, 10 we get x = 10 – 0 = 10 x = 10 – 5 = 5 x = 10 – 10 = 0
Given: the number of girls is 4 more than the number of boys Therefore y = x + 4 Putting x = – 4, 0, 4, and we get y = – 4 + 4 = 0 y = 0 + 4 = 4 y = 4 + 4 = 8
Graphical representation
Therefore, number of boys = 3 and number of girls = 7.
(ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen.
Ans. Let the cost of one pencil = Rs x Let the cost of one pen = Rs y 5 pencils and 7 pens together cost = Rs 50, Therefore 5x + 7y = 50 Subtracting 7y from both the sides we get 5x = 50 – 7y Dividing by 5 we get x = 10 – 7 y /5 Putting value of y = 5 , 10 and 15 we get x = 10 – 7 × 5/5 = 10 – 7 = 3 x = 10 – 7 × 10/5 = 10 – 14 = – 4 x = 10 – 7 × 15/5 = 10 – 21 = – 11
Given: 7 pencils and 5 pens together cost Rs 46 7x + 5y = 46 Subtracting 7x from both the sides we get 5y = 46 – 7x Dividing by 5 we get y = 46/5 – 7x/5 y = 9.2 – 1.4x Putting x = 0 , 2 and 4 we get y = 9.2 – 1.4 × 0 = 9.2 – 0 = 9.2 y = 9.2 – 1.4 (2) = 9.2 – 2.8 = 6.4 y = 9.2 – 1.4 (4) = 9.2 – 5.6 = 3.6
Graphical representation
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