Question

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.