Question

Determine the number of solutions to this system of linear equations:
4x+8y=12

3x+6y=9
(1 point)
Responses

infinite
infinite

2
2

1
1

0

Answer 1

To determine the number of solutions to the system of equations:

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

we will rearrange both equations to check their relationship.

First, let's simplify each equation.

Starting with the first equation:

\[
4x + 8y = 12
\]

Dividing the entire equation by 4:

\[
x + 2y = 3
\]

Next, for the second equation:

\[
3x + 6y = 9
\]

Dividing the entire equation by 3:

\[
x + 2y = 3
\]

Now, we can see that both equations simplify to the same equation:

\[
x + 2y = 3
\]

Since both equations are identical, they represent the same line in a 2D coordinate system. Therefore, there are infinitely many solutions, as any point on this line will satisfy both equations.

Thus, the correct response is:

**infinite**