To find the solution for the system of equations given in the table, we need to identify the point where the two equations intersect, which means both equations yield the same y-value for a given x-value.
The two equations given are:
- \( y = x + 6 \)
- \( y = 2x + 3 \)
We can look at the table and find where the y-values of both equations are equal.
From the table:
- For \( x = 0 \):
- \( y = x + 6 = 6 \)
- \( y = 2x + 3 = 3 \)
- For \( x = 1 \):
- \( y = x + 6 = 7 \)
- \( y = 2x + 3 = 5 \)
- For \( x = 2 \):
- \( y = x + 6 = 8 \)
- \( y = 2x + 3 = 7 \)
- For \( x = 3 \):
- \( y = x + 6 = 9 \)
- \( y = 2x + 3 = 9 \) (this is where they are equal)
- For \( x = 4 \):
- \( y = x + 6 = 10 \)
- \( y = 2x + 3 = 11 \)
At \( x = 3 \), both equations yield \( y = 9 \). Therefore, the solution to the system of equations is:
\((3, 9)\)