Question
Determine the number of solutions:
x + 2y = -4
4x + 8y = -16
x + 2y = -4
4x + 8y = -16
Answers
GPT-4o mini
To determine the number of solutions for the system of equations:
1. \( x + 2y = -4 \)
2. \( 4x + 8y = -16 \)
We can first manipulate the second equation to see its relationship to the first.
Notice that the second equation can be simplified. If we divide the entire equation \( 4x + 8y = -16 \) by 4, we get:
\[
x + 2y = -4
\]
This is exactly the same as the first equation.
Since both equations represent the same line, they are dependent. Thus, every point on the line \( x + 2y = -4 \) is a solution to the system.
Therefore, there are infinitely many solutions to this system of equations.
1. \( x + 2y = -4 \)
2. \( 4x + 8y = -16 \)
We can first manipulate the second equation to see its relationship to the first.
Notice that the second equation can be simplified. If we divide the entire equation \( 4x + 8y = -16 \) by 4, we get:
\[
x + 2y = -4
\]
This is exactly the same as the first equation.
Since both equations represent the same line, they are dependent. Thus, every point on the line \( x + 2y = -4 \) is a solution to the system.
Therefore, there are infinitely many solutions to this system of equations.