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in Mathematics by (60.8k points)
Using the method of integration, find the area of the region bounded by the lines : 2x + y = 4, 3x - 2y = 6, x - 3y + 5 = 0

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Best answer

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 in
ploted.
Shaded region is required region.
Required Area = Area of ΔABC

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