Answer: A: no solution
Explanation:
To use the elimination method, we want to add the two equations together in a way that eliminates one of the variables. We can do this by multiplying the second equation by 3 to get:
{6x + 15y = -12
{-6x - 15y = 27
Now, if we add the two equations together, the y terms will cancel out:
(6x + 15y) + (-6x - 15y) = -12 + 27
Simplifying:
0 = 15
This equation is never true, which means there is no solution to the system of equations. This can happen when the two equations represent parallel lines that never intersect. In this case, we can see that the two equations have the same slope (m=-2/5), so they are indeed parallel. Therefore, there is no point that satisfies both equations, and the system has no solution.