The lines representing the pair of equations 5x – 4y + 8 =0 and 7x + 6y -9 = 0
Are parallel
Are coincident
Intersect at a point
None of these
Answers
Given : pair of equations 5x – 4y + 8 =0 and 7x + 6y -9 = 0
To Find : The lines representing the pair are parallel , coincident , Intersect at a point or none of these
Solution:
Two lines
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
parallel if a₁/a₂ = b₁/b₂
Coincident if a₁/a₂ = b₁/b₂ = c₁ / c₂
Intersect at a point if a₁/a₂ ≠ b₁/b₂
Lets check for
5x – 4y + 8 =0
7x + 6y -9 = 0
a₁/a₂ = 5/7
b₁/b₂ = - 4/6
c₁ / c₂ = 8/-9
5/7 ≠ - 4/6
a₁/a₂ ≠ b₁/b₂
=> lines intersect at a point
Additional info:
15x - 12y + 24 + 14x + 12y - 18 = 0
=> 29x = -6
=> x = -6/29
35x - 28y + 56 = 35x + 30y - 45
=> 58y = 101
=> y = 101/58
intersection point ( -6/29 , 101/58)
5x – 4y + 8 =0 and 7x + 6y -9 = 0 lines intersect at a point
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Answer:
Given : pair of equations 5x – 4y + 8 =0 and 7x + 6y -9 = 0
To Find : The lines representing the pair are parallel , coincident , Intersect at a point or none of these
Solution:
Two lines
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
parallel if a₁/a₂ = b₁/b₂
Coincident if a₁/a₂ = b₁/b₂ = c₁ / c₂
Intersect at a point if a₁/a₂ ≠ b₁/b₂
Lets check for
5x – 4y + 8 =0
7x + 6y -9 = 0
a₁/a₂ = 5/7
b₁/b₂ = - 4/6
c₁ / c₂ = 8/-9
5/7 ≠ - 4/6
a₁/a₂ ≠ b₁/b₂
=> lines intersect at a point