Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. \[ \begin{array}{r}-x+6 y=3 \\ 3 x-18 y=-10\end{array} \] Answer Attempt 2 out of 2 Infinitely Many Solutions \( \begin{array}{l}\text { No Solutions }\end{array} \)

To solve this, you can use either the substitution or elimination methods. In this case, let's rewrite the equations in slope-intercept form. The first equation can be rearranged to \(y = \frac{1}{6}x + \frac{1}{2}\). The second equation simplifies to \(y = \frac{1}{6}x + \frac{5}{9}\). Since the slopes are the same but the y-intercepts are different, the lines are parallel, indicating that there are no solutions. When dealing with systems of equations, always remember to check for parallel lines by comparing slopes and intercepts. If the lines are parallel, they will never intersect, leading to the outcome of no solutions. This is a common mistake—assuming that parallel lines can intersect without first calculating their slopes!