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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?

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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.

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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?

Two lines passing through (1, 2) are
x + y = 3 ...(1)
and y = 2x ...(2)

Infinitely many more such lines can be found because the general equation of a line is ax + by + c = 0. For a given point (x, y) through which the line passes and for an arbitrary pair of values of a and b, c can be determined so as to satisfy ax + by + c = 0. This holds good for each given point and each arbitrary pair of values of a and b. Hence, infinitely many lines can be found passing through a given point.

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