Q27 of 45 Page 1

Using the method of integration, find the area of the region bounded by the lines
3x - 2y + 1 = 0, 2x + 3y - 21 = 0 and
x - 5y + 9 = 0.

Given; 3x - 2y + 1 = 0 …… (i)

2x + 3y - 21 = 0 …… (ii)


x - 5y + 9 = 0 …… (iii)


3×(i) + 2×(ii)


⇒ 13x − 39 = 0


⇒ x = 3.



∴ (3,5) is the intersection point of (i) and (ii).


(ii) − 2×(iii)


⇒ 13y − 39 = 0 ⇒ y = 3.



∴ (6,3) is the intersection point of (ii) and (iii).


(i) − 3×(iii)


⇒ 13y − 26 = 0


⇒ y = 2.



∴ (1,2) is the intersection point of (i) and (ii).



∴ Required Area is;







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