Using the method of integration find the area of the region bounded by lines:

2x + y = 4, 3x – 2y = 6 and x – 3y + 5 = 0

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Solution

The given equations of lines are

2x + y = 4 … (1)

3x – 2y = 6 … (2)

And, x – 3y + 5 = 0 … (3)

The area of the region bounded by the lines is the area of ΔABC. AL and CM are the perpendiculars on x-axis.

Area (ΔABC) = Area (ALMCA) – Area (ALB) – Area (CMB)

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Using the method of integration, find the area of the region bounded by lines
2x + y = 4, 3x - 2y = 6 and x - 3y + 5 = 0

2 x + y = 4, 3 x - 2 y = 6

x - 3 y + 5 = 0

3 x - 2 y + 1 = 0, 2 x + 3 y - 21 = 0

x - 5 y + 9 = 0

3 x - y - 3 = 0, 2 x + y - 12 = 0, x - 2 y - 1 = 0

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