Question

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

one solution, no solution, or infinite solutions

Answer 1

To determine whether the system of equations has one solution, no solution, or infinite solutions, we can analyze the equations:

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

First, we can simplify the second equation by dividing it by 3:

\[
\frac{3x - 6y}{3} = \frac{18}{3}
\]

This simplifies to:

\[
x - 2y = 6
\]

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

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

Since both equations represent the same line, there are infinitely many solutions that satisfy both equations. Therefore, the answer is:

**Infinite solutions.**