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Two lines in a coordinate plane have no points of intersection.
Which of these could be the equations of the lines?
A. 4x + 2y = 6 C. 4x + = 6
10x + 5y = 7 5x - 10y = 6
B. 4x + 2y = 6 D. 5x + 10y = 6
10x + 5y = 15 5x - 10y = 6
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(A) The lines have the same slope, but different y-intercepts.
So, these lines are parallel and have no common points.
(B) The lines have the same slope and the same y-intercepts.
So, these lines coincide.
(C) System (C) is written incorrectly, so I will not discuss/consider it.
(D) The lines have different slopes, so they intersect each other.
ANSWER. As far as I can make a conclusion considering cases (A), (B), and (D), lines (A) have no intersection points.
Solved.
Answer in the post by @lynnlo is incorrect.
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