Question 5 (Multiple Choice Worth 1 points) (05.02 LC) Solve the following system of equations: \( \begin{array}{l}-2 x+y=1 \\ -4 x+y=-1\end{array} \)

To solve the system of equations, you can use the elimination method. Start with the two equations: 1. \(-2x + y = 1\) 2. \(-4x + y = -1\) Next, you can eliminate \(y\) by subtracting the first equation from the second: \[ (-4x + y) - (-2x + y) = -1 - 1 \] This simplifies to: \[ -4x + 2x = -2 \\ -2x = -2 \\ x = 1 \] Now substitute \(x = 1\) back into one of the original equations to find \(y\): \[ -2(1) + y = 1 \\ -2 + y = 1 \\ y = 3 \] So, the solution to the system of equations is \(x = 1\) and \(y = 3\). Did you know? Systems of equations like this one aren't just for classrooms! Engineers, scientists, and economists use them to model real-world situations like supply and demand or engineering scenarios—it's basically putting math into action! For those curious about diving deeper, there are some fantastic resources available! Look into Algebra textbooks or online platforms like Khan Academy or Coursera, where you can explore lessons ranging from basic algebra to complex systems and their applications in various fields. Happy learning!