Answer:
The solutions are (-2, -8) and (8, 42).
Explanation:
The given equations
y= x^2 - 2x - 6
y= 4x + 10
both give y as a function of x. Thus, we can set them equal, which temporarily eliminates y as a variable.
Then: x^2 - 2x - 6 = 4x + 10
Group like terms on the left: x^2 - 6x - 16 = 0
Solve by factoring: x^2 - 6x - 16 = 0 = (x - 8)(x + 2) = 0. Then x = {-2, 8}.
Using y = 4x + 10, we find the corresponding y values one by one:
y = 4(-2) + 10 = -8 and y = 4(8) + 10 = 42.
The solutions are (-2, -8) and (8, 42).