Question

Solve the following system of linear equation graphically and shade the region between the two lines and x-axis:

3x + 2y − 4 = 0, 2x − 3y − 7 = 0

Answer 1

The given equations are:

3x + 2y − 4 = 0 .......(i)

2x − 3y − 7 = 0 .............(ii)

Putting x = 0 in equation (i) we get

`=> 3 xx 0 + 2y = 4`

=> y = 2

x = 0, y = 2

Putting y = 0 in equation (i) we get

`=> 3x + 2 xx 0 = 4`

=> x = 4/3

x = 4/3, y = 0

Use the following table to draw the graph.

x	0	4/3
y	2	0

The graph of (i) can be obtained by plotting the two points A(0,2), B(4/3, 0)

2x - 3y - 7 = 0........(ii)

Putting x = 0 in equation (ii) we get

`=> 2 xx 0 - 3y = 7`

=> y = -7/3

x = 0, y = -7/3

Putting y = 0 in equation (ii) weget

`=> 2x - 3 xx 0 = 7`

=>x = 7/2

x= 7/2 , y = 0

Use the following table to draw the graph.

x	0	7/2
y	-7/3	0

Draw the graph by plotting the two points  C(0,-7/3), D(7/2, 0) from table

The two lines intersect at P(2,-1). The area enclosed by the lines represented by the given equations and the coordinates x−axis and shaded the area in the graph.

Hence, x = 2 and y = -1 and is the solution.