Final answer:
The system of equations includes a quadratic and a linear equation. By using substitution or elimination, we can solve the system for x and y. After computing, we must check for extraneous solutions.
Step-by-step explanation:
The question asks to solve the system of equations (x-3)² + y² = 25 and 2x + y = 4. We need to use substitution or elimination methods to find the values of x and y that satisfy both equations. Since the second equation is already solved for y, it's convenient to express y as y = 4 - 2x and substitute this into the first equation.
To solve the first equation, expand (x-3)² to x² - 6x + 9. Then, substitute y with 4 - 2x and get x² - 6x + 9 + (4 - 2x)² = 25. Simplify this to find the values of x and then use these values to find corresponding y values. Checking for extraneous solutions is important as well since the squaring process could introduce them.