Given lines are
2x + y =4 … (i)
3x -2y = 6 … (ii)
x -3y + 5 = 0 … (iii)
For intersection point of (i) and (ii)
Multiplying (i) by 2 and adding with (ii), we get
Here, intersection point of (i) and (ii) is (2, 0).
For intersection point of (i) and (iii)
Multiplying (i) by 3 and adding with (iii), we get
Hence, intersection point of (i) and (iii) is (1, 2).
For intersection point of (ii) and (iii)
Multiplying (iii) by 3 and subtracting from (ii), we get
Hence intersection point of (ii) and (iii) is (4, 3).
With the help of intersecting points, required region DABC inploted.
Shaded region is required region.
Required Area = Area of ΔABC