Emaan used row operations on an augmented matrix representing a system of equations and obtained the following result. \( \left[\begin{array}{cc|c}1 & -2 & 7 \\ 5 & -10 & 35\end{array}\right] \) How many solutions does Emaan's system of equations have? A. 0 B. 1 C. 2 D. infinitely many

Emaan's augmented matrix can be simplified further using row operations. Notice that the second row (5, -10, 35) is simply 5 times the first row (1, -2, 7). This indicates that both equations represent the same line, leading to infinitely many solutions. Therefore, the answer is D. infinitely many. When two equations represent the same line in a two-dimensional space, it’s like dancing to the same tune – infinitely many points where they overlap! So, think of it as having a treasure map where the treasure is buried all along that line!