What are the solutions y=(x-3)(x+1) ,y=2x-8 (system of equations)

I guess you want to know the coordinates of intersection of the parabola with the linear equation; if so, expand Y=(x-3)(x+1)  =  y=x² -2x -3

To find the he points of intersection of y=x² - 2x -3 with y=2x-8, let the1st y equal the 2nd:
x² - 2x -3 = 2x -8 ===> x² - 4x + 5 =0
The discriminent Δ < 0, there is no roots (no zero value). hence there is no solution & the parabola and the line do not intersect