To find the solution for the system of equations given in the table, we need to identify the point where the two equations intersect.
The equations based on the table are:
- \(y = x + 6\)
- \(y = 2x + 3\)
We look for the pair of \(x\) and \(y\) values where the outputs from both equations are equal.
From the table:
- For \(x = 0\), \(y = 6\) (from the first equation) and \(y = 3\) (from the second equation) — not equal.
- For \(x = 1\), \(y = 7\) (first) and \(y = 5\) (second) — not equal.
- For \(x = 2\), \(y = 8\) (first) and \(y = 7\) (second) — not equal.
- For \(x = 3\), \(y = 9\) (first) and \(y = 9\) (second) — equal! This is a solution.
- For \(x = 4\), \(y = 10\) (first) and \(y = 11\) (second) — not equal.
Thus, the solution for the system of equations is \((3, 9)\).