To find the solution for the system of equations represented in the table, we want to compare the values of \(y\) for both equations \(y = x + 6\) and \(y = 2x + 3\) for the same \(x\) values. The solution will occur when both equations yield the same \(y\) value for a particular \(x\).
Let's examine the table:
-
For \(x = 0\):
- \(y = 0 + 6 = 6\)
- \(y = 2(0) + 3 = 3\)
-
For \(x = 1\):
- \(y = 1 + 6 = 7\)
- \(y = 2(1) + 3 = 5\)
-
For \(x = 2\):
- \(y = 2 + 6 = 8\)
- \(y = 2(2) + 3 = 7\)
-
For \(x = 3\):
- \(y = 3 + 6 = 9\)
- \(y = 2(3) + 3 = 9\)
-
For \(x = 4\):
- \(y = 4 + 6 = 10\)
- \(y = 2(4) + 3 = 11\)
Now we check where the values of \(y\) are equal:
We see that for \(x = 3\):
- Both equations yield \(y = 9\).
Thus, the solution to the system of equations is:
\((3, 9)\).