Question
This graph shows the lines for these equations:
3y=3x + 6
y = x + 2
How many solutions are there
No solution
One solution
Infinite solutions
3y=3x + 6
y = x + 2
How many solutions are there
No solution
One solution
Infinite solutions
Answers
Answer
you sure
Answered by
GPT-4o mini
To determine how many solutions there are for the equations \(3y = 3x + 6\) and \(y = x + 2\), we should first rewrite both equations in slope-intercept form (\(y = mx + b\)) for easier comparison.
1. **First equation:**
\[
3y = 3x + 6
\]
Dividing all terms by 3:
\[
y = x + 2
\]
2. **Second equation:**
\[
y = x + 2
\]
Now we see that both equations simplify to the same equation:
\[
y = x + 2
\]
Since both equations represent the same line, they have an infinite number of solutions (every point on the line is a solution).
Thus, the answer is **Infinite solutions**.
1. **First equation:**
\[
3y = 3x + 6
\]
Dividing all terms by 3:
\[
y = x + 2
\]
2. **Second equation:**
\[
y = x + 2
\]
Now we see that both equations simplify to the same equation:
\[
y = x + 2
\]
Since both equations represent the same line, they have an infinite number of solutions (every point on the line is a solution).
Thus, the answer is **Infinite solutions**.
Answered by
GPT-4o mini
Yes, I am sure.
To recap:
- The first equation, when simplified, becomes \(y = x + 2\).
- The second equation is already in the same form, \(y = x + 2\).
Since both equations represent exactly the same line (same slope and same y-intercept), every point on that line is a solution to both equations.
This means the system of equations has **infinite solutions**. If you have any further questions about this or need more clarification, feel free to ask!
To recap:
- The first equation, when simplified, becomes \(y = x + 2\).
- The second equation is already in the same form, \(y = x + 2\).
Since both equations represent exactly the same line (same slope and same y-intercept), every point on that line is a solution to both equations.
This means the system of equations has **infinite solutions**. If you have any further questions about this or need more clarification, feel free to ask!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.