two lines are given to be parallel the equation of one of the lines is 4x + 3y = 5,then one of the possible second parallel line is
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Given : two lines are given to be parallel the equation of one of the lines is 4x + 3y = 5, one of the possible second parallel line
To Find : one of the possible second parallel line
Solution:
Pair of linear equations
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Consistent
if a₁/a₂ ≠ b₁/b₂ (unique solution and lines intersects each others)
a₁/a₂ = b₁/b₂ = c₁/c₂ (infinite solutions and line coincide each other )
Inconsistent
if a₁/a₂ = b₁/b₂ ≠ c₁/c₂ ( No solution , lines are parallel to each other)
two lines are given to be parallel
Hence a₁/a₂ = b₁/b₂ ≠ c₁/c₂
4x + 3y = 5
=> parallel line can be
k₁ (4x + 3y ) = 5k₂ where k₁ ≠ k₂ and k₁ , k₂ are non zero real numbers
For example
4x + 3y = 6
4x + 3y = 7
8x + 6y = 5
8x + 6y = 6
These all can be possible second parallel line
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