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Linear Equations in Two Variables

Short Answer Type

71. Find three different solutions of the equation: 4x + 3y = 12, from its graph.

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72. Draw the graph of x + y = 3 and 2x + 2y = 8 on the same axes. What does the graph of these lines represent?

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73.

Draw graph of the following linear equations on the same axes

(i) x + y = 3
(ii) 3x – 2y = 4
Also shade the region formed by their graphs and y-axis.

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Long Answer Type

74. If x is the number of hours a labourer is on work and y his wages in rupees then y = 4x + 3. Draw the work wages graph of this equation. From the graph, find the wages of a labourer who puts in 4 hours of work.

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Short Answer Type

75. Draw the graph of the linear equation

straight y equals 2 over 3 straight x space plus 1 third

Check from the graph that (7, 5) is a solution of the linear equation.

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76. Draw the graph of linear equation 2x + y = 8on Cartesian plane. Write the coordinates of the points where this line intersects x-axis and y-axis.

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77. Rohit is driving his car at a uniform speed of 80 km per hour. Draw time-distance graph taking time along x-axis and distance along y-axis.

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78. A part of family budget on milk is constant and is fixed at र 500, while the other is variable and it depends on the need for milk at the rate oft 20 per litre. If extra milk taken is x litre and total expenditure on milk is रy, then write a linear equation for this problem. Draw its graph.

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79. Draw the graph of linear equation 4x + 3y = 36. From the graph, find the value of y when x = 3 and value of x when y = 6.

4x + 3y = 36 ....(1)
$rightwards double arrow$ 3y = 36 - 4x

$rightwards double arrow$ $straight y equals fraction numerator 36 minus 4 straight x over denominator 3 end fraction$

Table of solutions

X	0	9
y	12	0

We plot the points (0, 12) and (9,0) on a graph paper and join the same by a ruler to get the line which is the graph of the equation (1).
Mark a point P(3, 0) on x-axis. From P draw PQ || y-axis to intersect the graph at Q. From Q, draw QR || x-axis to intersect the y-axis at R(0, 8).

4x + 3y = 36

Hence, y = 8 when x = 3.

Again, mark a point A(0, 6) on y-axis. From A draw AB II x-axis to intersect the graph at B. From B, draw BC || y-axis to intersect x-axis at $straight C open parentheses 9 over 2 comma space 0 close parentheses$ .

Hence $straight x equals 9 over 2$ when y = 6

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80. Draw the graph of the equations x = 3 and 4x = 3y in the same graph. Find the area of the triangle formed by these two lines and the x-axis.

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