is there no solution, infinite solutions, or one solution to the following system of equations?

Question

x - 2y = 6
3x - 6y = 18

Answer 1

There is one solution to the given system of equations. By dividing the second equation by 3, we can rewrite it as:

x - 2y = 6
x - 2y = 6

These two equations are identical, which means that they represent the same line. Thus, they intersect at infinitely many points, but the equations are not dependent on each other. Therefore, the system has only one solution.