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Linear Equations in Two Variables

Long Answer Type

81. Draw the graph of the equation 2x + 3y = –5 and x + y = –1 in the same graph. Find the co-ordinates of the point of intersection of the two lines.

2x + 3y = -5
$rightwards double arrow$ 3y = - 5 - 2x

$rightwards double arrow$ $straight y space equals fraction numerator negative 5 minus 2 straight x over denominator 3 end fraction$

Table of solutions

X	–1	2
y	–1	–3

We plot the points (–1, –1) and (1, –3) on a graph paper and join the same by a ruler to get the line which is the graph of the equation 2x + 3y = –5.

x + y = –1

⇒ y = – 1 – x

Table of solutions

X	0	1
y	–1	–2

We plot the points (0, –1) and (1, –2) on the same graph paper and join the same by a ruler to get the line which is the graph of the equation x + y = –1.
From graph, we see that the coordinates of the point of intersection of the two lines are (2, –3).

2x + 3y = -5 3y = - 5 - 2x Table

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Short Answer Type

82.

Given the point (1,2), can you give the equation of a line on which it lies? How many such equations are there?

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83. You know that the force applied on a body is directly proportional to the acceleration produced in the body. Write an equation to express this situation and plot the graph of the equation.

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84. The following linear equation converts Fahrenheit temperature to Celcius

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

(i) If the temperature is 40°C, what is the temperature in Fahrenheit?
(ii) If the temperature is 95°F, what is the temperature in Celcius?
(iii) Is there a temperature which is numerically of same value in Fahrenheit and Celcius? If yes, find the temperature?

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85. Taxi fare in a city is र 8.00 for first kilometer and for the subsequent distance it is र 5.00 per km. Write a linear equation to represent this information in two variables taking distance covered as ‘x’ km and total fare as y (in र) and draw its graph. Find the distance travelled by a person if he spent र 63.00.

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86. Find the value of ‘m’ if x = 2, y = 1 is a solution of the equation 2x + 3y = m and represent it graphically.

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87. Given the point (1,2), find the equation of a line on which it lies. How many such equations are there? Write the equation in the form ax + by + c = 0.

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88. Draw the graph of linear equation 5y = 3x + 18 on Cartesian plane. From the graph check whether (–2,4) is the solution of linear equation or not.

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89. Give the equation of two lines passing through (3,4). How many more such lines are there and why?

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90. Draw the graph of the linear equation 3x + 2y = 12. Also find the points where this graph cuts x-axis and y-axis.

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