is this no solution, infinite solutions, or one solution. x - 2y = 6, 3x - 6y = 18

Answer 1

To determine the number of solutions for the system of equations

1. \( x - 2y = 6 \)
2. \( 3x - 6y = 18 \)

we can analyze the two equations.

First, let's rewrite the second equation:

\[ 3x - 6y = 18 \]

We can divide the entire equation by 3:

\[ x - 2y = 6 \]

Now we can see that both equations are actually the same:

1. \( x - 2y = 6 \)
2. \( x - 2y = 6 \) (after simplifying the second one)

Since both equations represent the same line, the system has infinitely many solutions, which are the points on that line.

Therefore, the answer is infinite solutions.