Question

When a system of equations involves two lines that
, there will be infinite solutions.

Answer 1

When a system of equations involves two lines that are **coincident**, there will be infinitely many solutions. This means that the two lines are essentially the same line, overlapping each other completely, so every point on one line is also a point on the other line, resulting in an infinite number of solutions. In terms of linear equations, this occurs when the equations are multiples of each other. For example:

1. \( y = 2x + 3 \)
2. \( 2y = 4x + 6 \) (which can be simplified to the same equation)

In this case, the two equations represent the same line, leading to infinitely many intersection points, i.e., solutions.