To solve this system of equations:
f(x) = x² - 2x + 3 ...(1)
f(x) = −5x + 1 ...(2)
We can substitute equation (2) into equation (1) to eliminate f(x):
-5x + 1 = x² - 2x + 3
Rearranging and simplifying:
x² - 3x + 2 = 0
Factoring:
(x - 1)(x - 2) = 0
Therefore, the solutions for x are x = 1 and x = 2.
To find the corresponding values of f(x), we substitute these values back into either equation (1) or (2):
For x = 1:
f(1) = (1)² - 2(1) + 3 = 2
For x = 2:
f(2) = (2)² - 2(2) + 3 = 3
Therefore, the solutions to the system of equations are (1, 2) and (2, 3), which represent the points where the two functions intersect.