Bot GPT 4-o mini 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:
- \( y = 2x + 3 \)
- \( 2y = 4x + 6 \) (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.
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