This graph shows the lines for these equations:

Question

3y=3x + 6

y=x+2

How many solutions are there for this system of equations?

No solutions

One solution

Infinite solutions

Answer 1

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.