Answer:
The ordered pair solutions for the system of equations are (-2, 5) and (1, 2).
Explanation:
How to determine ordered pair?
To determine if an ordered pair is a solution to two systems of equations, substitute the values of the variables into each equation. If an ordered pair makes both equations true, it is the solution of the system.
To find the ordered pair solutions for the system of equations, we need to solve the two equations simultaneously.
f(x) = x² + 1 ...(1)
f(x) = -x + 3 ...(2)
Setting the two equations equal to each other, we get:
x² + 1 = -x + 3
Rearranging this equation, we get:
x² + x - 2 = 0
Factoring this quadratic equation, we get:
(x + 2)(x - 1) = 0
Therefore, the solutions for x are x = -2 and x = 1.
Substituting these values of x into either equation (1) or (2), we get:
For x = -2: f(-2) = (-2)² + 1 = 5, and f(-2) = -(-2) + 3 = 5.
For x = 1: f(1) = 1² + 1 = 2, and f(1) = -1 + 3 = 2.
Therefore, the ordered pair solutions for the system of equations are (-2, 5) and (1, 2).