Problem 4: Select the statement that corr \( \begin{array}{l}5 x-y=15 \\ 2 x+y=9\end{array} \) A. There is no solution. B. There are infinitely many sc C. There is exactly one solutic D. There is exactly one solutic

To determine the nature of the solution for the system of equations \(5x - y = 15\) and \(2x + y = 9\), we can solve the system. By adding both equations, we can eliminate \(y\): - From the first equation: \(y = 5x - 15\). - Substitute \(y\) into the second equation: \(2x + (5x - 15) = 9\), which simplifies to \(7x - 15 = 9\). Solving for \(x\) gives \(x = \frac{24}{7}\), and plugging it back to find \(y\), we know there’s a unique point where both lines intersect. Thus, the correct answer is C. When working with systems of equations, don’t forget to graph them! Sometimes, visualizing equations can help you spot whether they are parallel, identical, or intersecting. It’s an easy way to see if there’s no solution, infinitely many, or just one solution! It's common to miscalculate during substitution. Always double-check your arithmetic, especially when you’re adding or subtracting equations. Small mistakes can lead you to the wrong conclusion about whether the lines intersect and how many solutions exist!