is 1,6 a solution to -x+y=5,y=(x-3)^2+2

Answer 1

To determine whether \( (1, 6) \) is a solution to the equations \( -x + y = 5 \) and \( y = (x - 3)^2 + 2 \), we need to check if this point satisfies both equations.

1. Check the first equation:
   \[ -x + y = 5 \] Substitute \( x = 1 \) and \( y = 6 \): \[ -1 + 6 = 5 \] This simplifies to: \[ 5 = 5 \] So, \( (1, 6) \) satisfies the first equation.

2. Check the second equation:
   \[ y = (x - 3)^2 + 2 \] Again, substitute \( x = 1 \): \[ y = (1 - 3)^2 + 2 \] This simplifies to: \[ y = (-2)^2 + 2 = 4 + 2 = 6 \] Thus, \( y = 6 \), which matches our point \( (1, 6) \).

Since \( (1, 6) \) satisfies both equations, we can conclude that \( (1, 6) \) is indeed a solution.