Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. -x+2y=-7 -4x+8y=-28 Answer Infinitely Many Solutions No Solutions One Solution

## Step 1: Convert Equations to Slope-Intercept Form<br />### The first equation is $-x + 2y = -7$. Solving for $y$, we get $y = \frac{1}{2}x - \frac{7}{2}$. The second equation is $-4x + 8y = -28$. Solving for $y$, we get $y = \frac{1}{2}x - \frac{7}{2}$.<br />## Step 2: Compare Slopes and Intercepts<br />### Both equations have the same slope $\frac{1}{2}$ and the same $y$-intercept $-\frac{7}{2}$. This means the lines are identical.<br />## Step 3: Determine the Number of Solutions<br />### Since the lines are identical, they overlap completely, indicating that there are infinitely many solutions.