Given lines are
5x - 2y - 10 = 0 ...(i)
x + y - 9 = 0 ...(ii)
2x - 5y - 4 = 0 ...(iii)
For intersecting point of (i) and (ii)
(i) + 2 × (ii) => 5x - 2y - 10 + 2x + 2y - 18 = 0
=> 7x - 28 = 0 => x = 4
Putting x = 4 in(i), we get
20 - 2y - 10 = 0 => y = 5
Intersecting point of (i) and (ii) is (4, 5).
For intersecting point of (i) and (iii)
(i) × 5 – (iii) × 2 => 25x - 10y - 50 - 4x + 10y + 8 = 0
=> 21x - 42 = 0 => x = 2
Putting x = 2 in (i) we get
10 - 2y - 10 = 0 => y = 0
i.e., Intersecting points of (i) and (iii) is (2, 0)
For intersecting point of (ii) and (iii)
2 × (ii) × (iii) => 2x + 2y - 18 - 2x + 5y + 4 = 0
=> 7y – 14 = 0 => y = 2
Putting y = 2 in (ii) we get
x + 2 - 9 = 0 => x = 7
Intersecting point of (ii) and (iii) is (7, 2).
Shaded region is required region.
Required Area
