Question

Solve the following system of linear equations 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.