Question

4x+8y=12 3x+6y=9 (1 point) Responses infinite infinite 1 1 2 2 0

Answer 1

To determine how many solutions the system of equations has, we can analyze the two equations:

1. \(4x + 8y = 12\)
2. \(3x + 6y = 9\)

We can simplify both equations.

Starting with the first equation:

1. Divide the entire equation by 4:
\[
x + 2y = 3
\]

Now, let's simplify the second equation:

2. Divide the entire equation by 3:
\[
x + 2y = 3
\]

Now we have:

1. \(x + 2y = 3\)
2. \(x + 2y = 3\)

Since both equations are identical, the lines represented by these equations coincide, meaning they overlap completely.

This system has **infinitely many solutions** (both equations represent the same line).

So, the answer is:

**infinite**.