Question Find the solution of the system of equations. \[ \begin{array}{r}-2 x+9 y=-17 \\ -x-3 y=-1\end{array} \] Answer Attempt 1 out of 2

To solve the system of equations, let's first rearrange the equations if needed and tackle them step by step. We have: 1. \(-2x + 9y = -17\) 2. \(-x - 3y = -1\) You could use either substitution or elimination. For simplicity, let's use elimination. First, we can multiply the second equation by 2 to align the \(x\) terms: \(-2x - 6y = -2\). Now we have: 1. \(-2x + 9y = -17\) 2. \(-2x - 6y = -2\) Subtract the second equation from the first: \((9y + 6y) = -17 + 2\) gives you \(15y = -15\). So, dividing both sides by 15 gives \(y = -1\). Now substitute \(y = -1\) back into one of the original equations to find \(x\). We'll use the second equation: \(-x - 3(-1) = -1\), simplifying gives \(-x + 3 = -1\). Thus, \(-x = -4\) leading to \(x = 4\). So, the solution to the system of equations is \((x, y) = (4, -1)\). In an engaging twist, solving systems of equations is like being a detective piecing together clues to find the hidden treasure of values! Plus, using methods like substitution and elimination is akin to having two different tools in your toolkit—each can help you crack the case, so choose wisely based on the clues at hand! For those eager to learn more, there are several engaging resources that dive deeper into systems of equations, such as Khan Academy and Purplemath. These platforms offer interactive exercises, vivid explanations, and a supportive community of learners to help you refine your skills while having fun!