Question

Solve graphically the system of linear equations:

4x − 3y + 4 = 0
4x + 3y − 20 = 0

Find the area bounded by these lines and x-axis.

Answer 1

The given equations are

4x − 3y + 4 = 0  ...........(i)

4x + 3y − 20 = 0 .............(ii)

Putting x = 0 in equation (i) we get

=> 4 xx 0 - 3y = -4

=> y = 4/3

x = 0, y = 4/3

Putting y = 0 in equation (i) we get

=> 4x -  3 xx 0 = -4

=> x = -1, y = 0

Use the following table to draw the graph.

x	0	-1
y	4/3	0

The graph of (i) can be obtained by plotting the points (0, 4/3), (−1, 0).

4x + 3y = 20 ..........(ii)

Putting x= 0 in equation (ii) we get

`=> 4 xx 0 + 3y = 20`

=> y = 20/3

x = 0, y = 20/3

Putting y= 0 in equation (ii) we get

`=> 4x + 3 xx 0 = 20`

=> x = 5

x = 5, y = 0

Use the following table to draw the graph.

x	0	5
y	20/3	0

Draw the graph by plotting the two points from table.

The two lines intersect at P(2,4)

Hence x = 2, y = 2 is the solution of the given equations.

Now,

Required area = Area of PBD

Required area = 1/2 (base x height)

Required area = 1/2 (BD x PM)

Required area = 1/2 (6 x 4)

Hence, the area = 12 sq. units