Hi everyone, I couldn’t could put things together why two non-equivalent linear equations would still intersect at one point? Specifically, why do we consider parallel lines as mentioned in the solution? Wouldn’t non-equivalent linear lines means you can’t solve them, hence they would never intersect?

Two lines are equivalent if and only if they are the same. For example, x + 2y = 10 and 2x + 4y = 20 are equivalent as both of them are the same thing.

Suppose two lines are *not* equivalent. What possible cases do you have? Try an example.

If they are parallel.

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I see I get what you mean. Non-equivalent simply means they are not the same line, not that they can be equated to be solved for identifying certain values.