Final answer:
To solve the system of equations y = -13x + 38 and y = x² - 10x - 2, set the equations equal to each other and solve the resulting quadratic equation. The solutions are (-5, 103) and (8, -54).
Step-by-step explanation:
To solve the system of equations y = -13x + 38 and y = x² - 10x - 2, we can set the two equations equal to each other:
x² - 10x - 2 = -13x + 38
Next, we rearrange the equation to standard form:
x² - 3x - 40 = 0
Now, we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula:
x² - 8x + 5x - 40 = 0
x(x - 8) + 5(x - 8) = 0
(x + 5)(x - 8) = 0
x = -5 or x = 8
Substituting these values into either equation, we can find the corresponding y-coordinates:
For x = -5: y = -13(-5) + 38 = 103
For x = 8: y = -13(8) + 38 = -54
Therefore, the coordinates in exact form are (-5, 103) and (8, -54).