Final answer:
To solve the given system of equations, we equate y = x² - 5x - 58 and y = -3x + 5 and simplify to x² - 2x - 63 = 0, which factors into two solutions (9, -22) and (-7, 26).
Step-by-step explanation:
The student has requested assistance with solving a system of equations. To solve the system y = x² - 5x - 58 and y = -3x + 5 algebraically, we can set the two equations equal to each other since they both represent y.
We get x² - 5x - 58 = -3x + 5. From here, we start the process of solving for x by moving all terms to one side to obtain a quadratic equation: x² - 2x - 63 = 0. This can be factored into (x - 9)(x + 7) = 0, yielding two solutions for x: x = 9 and x = -7.
Plugging these x-values back into either original equation, we find the corresponding y-values. For x = 9, y = -3(9) + 5 = -22; for x = -7, y = -3(-7) + 5 = 26. Thus, the solutions to the system of equations are (9, -22) and (-7, 26).