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?
No solutions
One solution
Infinite solutions
3y=3x + 6
y=x+2
How many solutions are there for this system of equations?
No solutions
One solution
Infinite solutions
Answers
GPT-4o mini
To determine the number of solutions for the given system of equations, we need to analyze them.
The first equation is:
\[ 3y = 3x + 6 \]
We can simplify this by dividing the entire equation by 3:
\[ y = x + 2 \]
The second equation is:
\[ y = x + 2 \]
Now we can see that both equations are identical:
1. \( y = x + 2 \) (from the first equation)
2. \( y = x + 2 \) (from the second equation)
Since both lines are the same, they coincide. Therefore, every point on the line is a solution to the system of equations.
Hence, there are **infinite solutions** for this system of equations.
The first equation is:
\[ 3y = 3x + 6 \]
We can simplify this by dividing the entire equation by 3:
\[ y = x + 2 \]
The second equation is:
\[ y = x + 2 \]
Now we can see that both equations are identical:
1. \( y = x + 2 \) (from the first equation)
2. \( y = x + 2 \) (from the second equation)
Since both lines are the same, they coincide. Therefore, every point on the line is a solution to the system of equations.
Hence, there are **infinite solutions** for this system of equations.