to the lines of equation 2x+y+4=0 and x+2y-5=0 intersect? justify your answer
Answers
a1/a2 != b1/b2 then lines will intersect check condition
2/1 != 1/2 so lines will intersect and they will have a unique solution
The two lines 2x + y + 4 = 0 and x + 2y - 5 = 0 intersect each other because they have a common point (-13/3, 14/3).
Given:
The equation of the first line: 2x + y + 4 = 0
The equation of the second line: x + 2y - 5 = 0
To Find:
If the two given lines 2x + y + 4 = 0 and x + 2y - 5 = 0 intersect.
Solution:
The equation of the first line: 2x + y + 4 = 0
∴ y = (-4 - 2x) - Eq.(i)
→ The equation of the second line: x + 2y - 5 = 0 - Eq.(ii)
∴ Putting the value of 'y' from Eq.(i) in to Eq.(ii):
∴ x + 2y - 5 = 0
∴ x + 2(-4 - 2x) - 5 = 0
∴ x - 8 - 4x - 5 = 0
∴ -3x - 13 = 0
∴ -3x = 13
∴ x = -13/3
→ Now calculating the value of 'y':
∴ y = (-4 - 2x)
∴ y = [-4 - 2(-13/3)]
∴ y = [-4 + 26/3]
∴ y = 14/3
→ Therefore the value of 'x' is -13/3 and value of 'y' is 14/3. Hence the point of intersection of these two lines would be (-13/3, 14/3).
→ As these two lines have a common point (-13/3, 14/3) which is their point of intersection. Hence it can be said that these lines intersect each other. Therefore these lines are intersecting lines.
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