Given,
Equations of 3 straight lines:
2x + y - 1 = 0
4x + 3y + 5 = 0
5x + 4y + 8 = 0
We first find the point of intersection of any 2 lines and then check whether it satisfies the 3rd equation. If it does, we say that the 3 lines intersect ay a common point.
2x + y - 1 = 0 ---(1)
4x + 3y + 5 = 0 ---(2)
Multiplying (1) with 3, we get
6x + 3y - 3 = 0 ---(4)
Subtracting (2) - (4), we get
4x + 3y + 5 - (6x + 3y - 3) = 0
⇒ 4x - 6x + 5 + 3 = 0
⇒ - 2x + 8 = 0
⇒ 2x = 8
⇒ x = 4
Substituting x in eq, (1), we get
2 x 4 + y - 1 = 0
⇒ 8 + y - 1 = 0
⇒ y = -7
Hence (4, -7) is the point of intersection of the equations 1 and 2
5x + 4y + 8 = 0 ---(3)
Checking whether (4, -7) satisfies equation (3), we can say
5 x 4 + 4 x (-7) + 8
⇒ 20 - 28 + 8
⇒ 0
Since it satisfies eq (3), we say they have a common point of intersection (4, -7)
Hence,
The three lines represented by the equations:
2x + y - 1 = 0
4x + 3y + 5 = 0
5x + 4y + 8 = 0,
intersect at the common point (4, -7)
