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** (meaning they lie on top of each other), there will be infinitely many solutions. This occurs when the two equations represent the same line in the coordinate plane. In such cases, every point on the line is a solution to the system of equations. Mathematically, this can happen when one equation is a scalar multiple of the other.

For example, the lines represented by the equations:

1. \( y = 2x + 3 \)
2. \( 2y = 4x + 6 \)

are coincident, as the second equation simplifies to the same equation as the first when divided by 2. Thus, there are infinitely many solutions along the line \( y = 2x + 3 \).