Potential Errors Found In Flashcards?

Hello! I believe I have found some potential errors in the coordinate geometry flashcards in Group 7.

If I am wrong and these are not errors, can you help be understand why my reasoning is flawed?

On the Parallel/Perpendicular Flashcard:
The fun fact states that “perpendicular lines always intersect and it’s possible for the intersection to occur at either the x or y intercept, but not both.” But what if they intersect at the origin? Would that not be considered intersecting at both the x and y intercepts? If not, why not?

Then; on the next slide System of Equations:
for the Substitution demonstration, 4x + y is in parentheses after the 9 in the substituted equation 5x + 9(4x + y). If this is correct, why are we including the y and not using (4x + 7)?

Im sorry if I misinterpreted or misunderstood the material as a mistake. Thank you for taking the time to help me understand.

They intersect at the origin, no? Two lines can at most intersect at one point.

Would be helpful if you could post a picture of whatever you’re referring to here

Yes, it’s a typo and it should be 4x + 7 instead of 4x + y