Problem 2: Select the statement that \( \begin{array}{l}2 x-y=4 \\ 4 x-2 y=10 \\ \text { A. There is no solution. } \\ \text { B. There are infinitely mat } \\ \text { C. There is exactly one sc } \\ \text { D. There is exactly one sc }\end{array} \)

To analyze the system of equations, let's simplify the second equation. Notice that \(4x - 2y = 10\) can be divided by 2 to yield \(2x - y = 5\). Now we have two equations: 1. \(2x - y = 4\) 2. \(2x - y = 5\) These two equations represent parallel lines because they have the same slope but different y-intercepts. Parallel lines never intersect, which means there is no solution to this system. Therefore, the correct answer is: A. There is no solution. For another exciting exploration, here’s a tip: Always look for ways to simplify equations! Reducing them can make it easier to spot relationships, such as whether lines are parallel or overlapping. And remember, with systems of equations, it’s all about the intersections—like trying to find where two paths cross in a crowded park! As a common mistake, students often forget to check for equivalent equations. Just because the coefficients look different doesn’t mean the equations aren't just scalar multiples of one another, leading to potentially missing situations where solutions do exist! Always double-check!