\( \begin{array}{l}y+3=2 x \\ y+4=3 x\end{array} \) If you use the comparison method to solve the given system, what is the resulting equatio \( 2 x-3=3 x-4 \) \( y+3=y+4 \) \( 2 x+3=3 x+4 \)

To solve the system using the comparison method, you first need to express both equations in the form \(y = mx + b\). Rearranging both, you get: 1. From \(y + 3 = 2x\), we find \(y = 2x - 3\). 2. From \(y + 4 = 3x\), we find \(y = 3x - 4\). Now, set the two expressions for \(y\) equal to each other: \(2x - 3 = 3x - 4\). So, the resulting equation is indeed \(2x - 3 = 3x - 4\). Remember, this means you did it right and the solution will guide you to the intersection point of both lines! In solving systems of equations via comparison, always take care to correctly isolate \(y\) first. A common mistake is misaligning terms, which can lead to confusion. For instance, if you accidentally set \(2x - 4 = 3x - 3\), you would derive an incorrect equation that might lead you astray. Double-checking your rearrangements is a smart way to ensure accuracy!