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 solve the system of equations represented in the table, we need to find the values of \( x \) and \( y \) such that both equations are satisfied. The equations given are:

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

We can substitute the y-values from the table into these equations and find the matching \( (x, y) \) pair.

Let’s look at the values in the table:

• For \( x = 0 \):

  • \( y = x + 6 \) ⇒ \( y = 6 \)
  • \( y = 2x + 3 \) ⇒ \( y = 3 \)

• For \( x = 1 \):

  • \( y = x + 6 \) ⇒ \( y = 7 \)
  • \( y = 2x + 3 \) ⇒ \( y = 5 \)

• For \( x = 2 \):

  • \( y = x + 6 \) ⇒ \( y = 8 \)
  • \( y = 2x + 3 \) ⇒ \( y = 7 \)

• For \( x = 3 \):

  • \( y = x + 6 \) ⇒ \( y = 9 \)
  • \( y = 2x + 3 \) ⇒ \( y = 9 \)

• For \( x = 4 \):

  • \( y = x + 6 \) ⇒ \( y = 10 \)
  • \( y = 2x + 3 \) ⇒ \( y = 11 \)

The only \( (x, y) \) pair that makes both equations true simultaneously is when \( x = 3 \) and \( y = 9 \).

Thus, the solution for the system is:

\((3, 9)\).