Question Watch Video Solve the system of equations \( -x-4 y=-23 \) and \( 2 x-y=1 \) by combining the equations. \[ \begin{array}{c} 4(-x-4 y=-23) \\ 4(2 x-y=1) \\ -4 x-16 y=-92 \\ 8 x-4 y=4 \\ 4 x+\circ y= \end{array} \] \( \square \)

Let's dive into solving those equations! To combine the provided equations, we can add them together after making sure they line up properly. First, we rewrite our equations: 1. \( -x - 4y = -23 \) 2. \( 2x - y = 1 \) Now, we'll multiply the second equation by 4 to align the \(y\) coefficients, giving us: \[ 8x - 4y = 4 \] Next, we add it to the transformed first equation, taking care to line up the terms: \[ -4x - 16y = -92 \\ 8x - 4y = 4 \] When you add these, the \(x\) terms will combine and simplify nicely. Combining gives us: \[ 4x - 20y = -88 \] And then dividing the entire equation by 4 leads us to: \[ x - 5y = -22 \] Now you have a neat new equation to work with along with one of the original equations. Solving the system becomes much easier from here! Finally, on to a little fun with equations! Did you know solving systems of equations can be visualized on a graph as finding the intersection of two lines? It’s like a treasure hunt to find where the two paths cross! Plus, practice makes perfect. The more you solve, the faster you'll get at spotting those intersections. Keep going!