Final answer:
To solve the system of equations, we can use the method of substitution. However, when we substitute the expression for x in the second equation, we get an equation that is not true, indicating that the system has no solution.
Step-by-step explanation:
To solve the system of equations given by 5x - 2y = -6 and 15x - 6y = 6, we can use the method of substitution. First, we can solve one of the equations for either variable, then substitute that expression into the other equation to solve for the other variable. Let's solve the first equation for x:
5x - 2y = -6
5x = 2y - 6
x = (2y - 6)/5
Now, substitute this expression for x in the second equation:
15((2y - 6)/5) - 6y = 6
6y - 18 - 6y = 6
-18 = 6
This leads to the equation -18 = 6, which is not true. Therefore, the system of equations has no solution. So, the correct answer is C. No solution.