To determine if the point (1, 6) is a solution to the system of equations, we need to check if it satisfies both equations.
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First equation:
\(-x + y = 5\)
Plugging in \(x = 1\) and \(y = 6\):
\(-1 + 6 = 5\)
\(5 = 5\)
This equation holds true. -
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.