Can any one elaborate on the intuition of this question? Thanks

Try a few examples.

The question explores the different outcomes when comparing linear equations. Let’s simplify the explanations for each option:

A) Two lines never intersect: This suggests parallel lines. For linear equations, this happens when they have identical slopes but different y-intercepts. It’s a valid scenario for “non-equivalent” lines, as they don’t overlap.

B) The equations intersect at exactly one point: This is a common characteristic of linear equations. Since they are straight lines, they can intersect at one point unless they are parallel (option A).

C) The equations intersect at exactly two points: Linear equations, being straight lines, cannot intersect at more than one point. This option is incorrect because linear lines don’t curve or bend.

D) The equations intersect at every point: This would mean the lines are identical. However, the question specifies non-equivalent equations, ruling out the possibility of them intersecting everywhere.

In summary, options A and B are possible for linear equations, while C and D are not, given the condition of the equations being non-equivalent.

Please let me know if this is clear, I am also striving for a high quant score and all feedback helps me improve!

I wish you the best in your journey as well, good luck!