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

Answer 1

you sure

Answer 2

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**.

Answer 3

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!