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Question

Draw the graphs of the linear equations 4x − 3y + 4 = 0 and 4x + 3y −20 = 0. Find the area bounded by these lines and x-axis.

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Solution

We are given,

We get,

Now, substituting in ,we get

Substituting in ,we get

Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the given equation

x

0

–1

y

0

Plotting E(0, ) and A(-1,0) on the graph and by joining the points , we obtain the graph of equation .

We are given,

We get,

Now, substituting in ,we get

Substituting in ,we get

Thus, we have the following table exhibiting the abscissa and ordinates of points on the line represented by the given equation

x 0 5
y 0

Plotting D(0, ) and B(5,0) on the graph and by joining the points , we obtain the graph of equation .

By the intersection of lines formed by and on the graph, triangle ABC is formed on x axis.

Therefore,

AB at x axis is the base of triangle ABC having AB = 6 units on x axis.

Draw CF perpendicular from C on x axis.

CF parallel to y axis is the height of triangle ABC having CF = 4 units on y axis.

Therefore,

Area of triangle ABC, say A is given by


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