Which of the following uses the substitution method to solve linear-quadratic system y = x^2 - 4x - 41, y = 4?
• (-5,4)
• (5,4) and (-9,4)
• (9,4)
• (-5, 4) and (9,4)
To use the substitution method, we substitute the value of y from the second equation into the first equation. This gives us x^2 - 4x - 41 = 4. Simplifying this equation gives us x^2 - 4x - 45 = 0. Factoring this equation gives us (x - 9)(x + 5) = 0. Therefore, x = 9 or x = -5.
Substituting these values back into the second equation, we get y = 4 for both x = 9 and x = -5.
Therefore, the correct answer is (-5, 4) and (9, 4).