Question

which represents the solution(s) of the system of equations, $y = x^2 - x + 1$ and $y = x$? determine the solution set by graphing.\
\bigcirc\\ (1, 1)\
\bigcirc\\ (0, 1) and (1, 1)\
\bigcirc\\ (0, 0) and (1, 1)\
\bigcirc\\ no solutions

Explanation:

Step1: Set equations equal

Set \( y = x^2 - x + 1 \) and \( y = x \) equal: \( x = x^2 - x + 1 \).

Step2: Rearrange into quadratic

Rearrange to \( x^2 - 2x + 1 = 0 \).

Step3: Solve quadratic

Factor: \( (x - 1)^2 = 0 \), so \( x = 1 \).

Step4: Find y - value

Substitute \( x = 1 \) into \( y = x \), get \( y = 1 \). So the solution is \( (1, 1) \).

Answer:

(1, 1)