Graph the system below and write its solution. \[ \begin{array}{l}x+4 y=4 \\ y=-\frac{1}{4} x+3\end{array} \] Note that you can also answer "No solution" or "Infinitely many" solutions.

To solve the system of equations, let’s start by graphing both lines: 1. For the first equation \( x + 4y = 4 \), you can rewrite it in slope-intercept form: \[ 4y = -x + 4 \] \[ y = -\frac{1}{4}x + 1 \] This line has a slope of \(-\frac{1}{4}\) and a y-intercept at \( (0, 1) \). 2. The second equation is already in slope-intercept form: \[ y = -\frac{1}{4}x + 3 \] This line also has a slope of \(-\frac{1}{4}\) but with a y-intercept at \( (0, 3) \). Now, let's graph both equations. Both lines have the same slope, which indicates they are parallel. Since they also have different y-intercepts, they will never intersect. This implies that the system has **no solution**. There is no point \((x, y)\) that satisfies both equations simultaneously. To visualize this: - The line from the first equation starts at (0, 1) and slopes down to the right. - The line from the second equation starts higher at (0, 3) and slopes down to the right as well. Because they never meet, that's why we conclude: **No solution**!