Question

If the pair of linear equations a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0,(a₁,b₁,c₁,a₂,b₂ and c₂ are all real numbers and a₁,b₁,a₂,b₂, are not equal to zero) represents parallel lines, then which of the following is correct?

A. a₁/a₂=b₁/b₂≠c₁/c₂
B. a₁/a₂≠b₁/b₂
C. a₁/a₂=2b₁/b₂=2c₁/c₂
D. a₁/a₂=b₁/b₂=c₁/c₂

Answer 1

For the given pair of linear equations to represent parallel lines, we must have a₁/a₂ = b₁/b₂. Therefore, the correct option is A. a₁/a₂ = b₁/b₂ ≠ c₁/c₂.

Step-by-step explanation:

To determine which of the options is correct, we need to analyze the conditions for the given pair of linear equations to represent parallel lines. In general, two lines are parallel if and only if their slopes are equal. The slope of a line can be found by dividing the coefficient of x by the coefficient of y in the equation. Therefore, for the given pair of equations to represent parallel lines, we must have a₁/a₂ = b₁/b₂. Therefore, the correct option is A. a₁/a₂ = b₁/b₂ ≠ c₁/c₂.