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Linear Equations in Two Variables

Long Answer Type

61. Yamini and Fatima, two students of Class IX of a school, together contributed Rs 100 towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear equation which satisfies this data. (You may take their contributions as Rs x and Rs y.) Draw the graph of the same.

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Short Answer Type

62. In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius:

straight F equals open parentheses 9 over 5 close parentheses straight C plus 32

Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for y-axis.

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63. In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius:

straight F equals open parentheses 9 over 5 close parentheses straight C plus 32

If the temperature is 30°C, what is the temperature in Fahrenheit?

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64. In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius:

straight F equals open parentheses 9 over 5 close parentheses straight C plus 32

If the temperature is 95°F, what is the temperature in Celsius?

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65. In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius:

straight F equals open parentheses 9 over 5 close parentheses straight C plus 32

If the temperature is 95°F, what is the temperature in Celsius?

114 Views

66. In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius:

straight F equals open parentheses 9 over 5 close parentheses straight C plus 32

Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

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67. Draw the graph of the equation 3x + y = 8. Use it to find some solutions of the equation and check from the graph whether x = 2, y = 2 is a solution.

3x + y = 8
⇒ y = 8 – 3x
Table of solutions

x	0	3
y	8	-1

We plot the points (0, 8) and (3, – 1) on the graph paper and join the same by a ruler to get the line which is the graph of the equation 3jc + y = 8.

3x + y = 8⇒ y = 8 – 3xTable of solutions

x

0

3

y

8

-1

∵ The point (2, 2) lies on the graph.

∴ x = 2, y = 2 is a solution of the given equation.

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68. Force applied on a body is directly proportional to the acceleration produced in the body. Write an equation to express the situation and plot the graph of the equation taking constant to be 5 units.

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69. Shade the triangle formed by the graphs of 2x – y = 4, x + y = 2 and the y-axis. Write the coordinates of vertices of the triangle.

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70. Give the equations of two lines passing through (1, 2). How many more such lines are there and why?

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