Question

Question

Use the table to answer the question.

x-value y-value if y=x+6
y-value if y=2x+3

0 6 3
1 7 5
2 8 7
3 9 9
4 10 11
A system of equations is displayed in the table. What is the solution for the system?

(1 point)
(
,
)

Answer 1

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:

1. \(y = x + 6\)
2. \(y = 2x + 3\)

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 \((3, 9)\).