The given system of equations:

2x-3y+6=0 and 2x+3y-18=0

Now,2x-3y+6=0

y= (2x+6)/3

When x=0, then y=2

When x=-3, then y=0

Thus, we have the following table:

We have

2x+3y-18=0

X= 18−3y/2

When y=2, then x=6

When y=6, then x=0

Thus, we have the following table:

Graph of the given system of equations:

Clearly, the two lines intersect at A(3,4) .Hence x=3 and y=4 is the solution of the given system of equations.

From the graph, we have

AD=x-coordinate point A(3,4) =3

BC=6-2 = 4

Area of the shaded region = 1/2×base×altitude

= 1/2×4×3

= 6 sq. units