-x + y = 5
y = (x-3)2 + 2
Is (1, 6) a solution to the system of equations? Explain.
To determine if (1, 6) is a solution to the system of equations, we substitute the values of x and y into each equation and check if they are satisfied.
For the first equation:
-x + y = 5
Substituting x = 1 and y = 6, we get:
-(1) + 6 = 5
6 - 1 = 5
5 = 5
The first equation is satisfied.
For the second equation:
y = (x-3)^2 + 2
Substituting x = 1 and y = 6:
6 = (1-3)^2 + 2
6 = (-2)^2 + 2
6 = 4 + 2
6 = 6
The second equation is also satisfied.
Since both equations are satisfied, (1,6) is a solution to the system of equations.