Determine if the following system of equations has no solutions, infinitely many solutions or
exactly one solution.

Answer
One Solution
Infinitely Many Solutions

The given system of equations can be manipulated to determine its solution set. If we multiply the first equation by , we end up with , which is exactly the second equation. This indicates that both equations represent the same line in the coordinate system. Therefore, the two equations have infinitely many solutions that lie on this line.

To visualize the relationship between these two equations, you can graph both on the same coordinate plane. Since both of them overlap entirely, you’ll see that they are not just intersecting at one point - instead, every point on that line is a solution! This means that there’s no unique solution, but rather an entire set of solutions to choose from.