Consider the following system of equations:

Question

-x+y=5
y=(x-3)^2+2

A. Is (1, 6) a solution to the system of equations? Explain.

Answer 1

To determine if the point (1, 6) is a solution to the system of equations, we need to check if it satisfies both equations.

1. First equation:
   \(-x + y = 5\)
   Plugging in \(x = 1\) and \(y = 6\):
   \(-1 + 6 = 5\)
   \(5 = 5\)
   This equation holds true.

2. Second equation:
   \(y = (x - 3)^2 + 2\)
   Plugging in \(x = 1\) and \(y = 6\):
   \(6 = (1 - 3)^2 + 2\)
   \(6 = (-2)^2 + 2\)
   \(6 = 4 + 2\)
   \(6 = 6\)
   This equation also holds true.

Since both equations are satisfied by the point (1, 6), we conclude that (1, 6) is indeed a solution to the system of equations.