Question

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

2x + 3y = 12

x – y = 1

Answer 1

The given equation is

2x + 3y = 12  ......(i)

x − y = 1  .......(ii)

Putting x = 0 in equation (i) we get

`=> 2xx0 + 3y = 12`

`=> y = 4`

Putting y = 0 in equation (i) we get

`=> 2x + 3 xx 0 = 12`

`=> x = 6`

x = 6, y = 0

Use the following table to draw the graph.

x	0	6
y	4	0

Draw the graph by plotting the A(0, 4), B(6, 0) two points from table

x - y = 1 ....(ii)

Putting x = 0 in equation (ii) we get

`=> 0 - y = 1`

`=> y = -1`

x = 0, y = -1

Putting y = 0 in equation (ii) we get

`=> x - 0 = 1`

`=> x = 1`

x = 1, y = 0

Use the following table to draw the graph.

x	0	1
y	-1	0

Draw the graph by plotting the two points C(0, -1), D(1, 0) from table.

The two lines intersect at P(3, 2). The region enclosed by the lines represented by the given equations and x-axis are shown in the above figure

Hence, x = 3 and y = 2 is the solution.