Question

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**.