(1)) Is \( (-9,-10) \) a solution to this system of equations? \( \begin{array}{l}17 x-17 y=17 \\ 6 x-4 y=-14 \\ \text { (1) yes no }\end{array} \)

To see if \( (-9,-10) \) is a solution, we can substitute these values into both equations. For the first equation \( 17(-9) - 17(-10) = 17 \) simplifies to \( -153 + 170 = 17 \), which is true. For the second equation \( 6(-9) - 4(-10) = -14 \), we have \( -54 + 40 = -14 \), which is also true. Since both equations hold true, the answer is yes! Now why not check some real-world scenarios where such systems might pop up! Imagine you're a baker trying to optimize the ingredients for two different types of bread. The relationships can be modeled via such systems, allowing you to find the ideal balance while saving money and keeping your customers happy. Lastly, if you're ever unsure about solving a system of equations, be careful with your signs! A common mistake is losing track of negative signs when substituting values—we've all been there! Taking a moment to double-check your arithmetic can save you from that pesky error.