Question
Extension
This graph shows the lines for these equations:
3y=3x + 6
y = x + 2
How many solutions are there for this system of equations?
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:
1. \( 3y = 3x + 6 \)
2. \( y = x + 2 \)
we can first simplify the first equation:
1. Divide both sides of the first equation by 3:
\[
y = x + 2
\]
Now we have both equations in the same form:
1. \( y = x + 2 \)
2. \( y = x + 2 \)
Since both equations are identical, they represent the same line. Therefore, every point on this line is a solution to the system of equations.
This means there are infinitely many solutions to this system of equations since they are the same line.
1. \( 3y = 3x + 6 \)
2. \( y = x + 2 \)
we can first simplify the first equation:
1. Divide both sides of the first equation by 3:
\[
y = x + 2
\]
Now we have both equations in the same form:
1. \( y = x + 2 \)
2. \( y = x + 2 \)
Since both equations are identical, they represent the same line. Therefore, every point on this line is a solution to the system of equations.
This means there are infinitely many solutions to this system of equations since they are the same line.