Question
This graph shows the lines for these equations: 3y=3x + 6 y = x + 2 How many solutions are there for this system of equations?
Answers
GPT-4o mini
To determine how many solutions there are for the system of equations given by \( 3y = 3x + 6 \) and \( y = x + 2 \), we can start by simplifying the first equation.
The first equation \( 3y = 3x + 6 \) can be simplified by dividing every term by 3:
\[
y = x + 2
\]
Now we have two equations:
1. \( y = x + 2 \)
2. \( y = x + 2 \)
Both equations are identical, meaning they represent the same line. In terms of a system of equations, this indicates that every point on the line is a solution. Therefore, there are infinitely many solutions for this system of equations.
So, the answer is:
**Infinitely many solutions.**
The first equation \( 3y = 3x + 6 \) can be simplified by dividing every term by 3:
\[
y = x + 2
\]
Now we have two equations:
1. \( y = x + 2 \)
2. \( y = x + 2 \)
Both equations are identical, meaning they represent the same line. In terms of a system of equations, this indicates that every point on the line is a solution. Therefore, there are infinitely many solutions for this system of equations.
So, the answer is:
**Infinitely many solutions.**