Answer:
A. No solutions
Explanation:
When working with a system of equations, the solutions are wherever the lines intersect.
Slope
To find the intersection, we can use the slopes. To find the slopes we first need to write the first equation (-6x + y = 6) in slope-intercept form.
To find the new equation add -6x to both sides
Using this information we can see that the slopes of both lines are the same; however, the y-intercepts are different. This means that the lines are different, parallel lines. Remember that parallel lines never intersect. Since these lines will never intersect, there must be no solutions.
Graph
Another way to find the solution is by looking at the lines you are given. However, it is important to understand that this is less accurate than the method above because it is possible that the lines could intersect outside of the range of the graph.
By looking at the graph we can see that the lines never intersect; additionally, the lines appear parallel. So, if you cannot use the method above, this is a good way to make an educated guess.