If a system of linear equations has infinitely many solutions

A dependent system has infinitely many solutions. The lines are coincident. They are the same line, so every coordinate pair on the line is a solution to both equations.

An infinite solution has both sides equal. For example, 6x + 2y - 8 = 12x +4y - 16. If you simplify the equation using an infinite solutions formula or method, you'll get both sides equal, hence, it is an infinite solution.