Which steps could be part of the process in algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x – 10? check all that apply.

y = x2 + 5x + 10
y + 5x = x2 + 10 + 4x – 10
4x – 10 = x2 – 5x + 10
0 = x2 – 9x
0 = x2 – 9x + 20
one x-value of a solution to the system is 4.

That would be :
 4x – 10 = x2 – 5x + 10  ( y = 4x - 10 is substitute for y)

 PROOF:        y + 5x = x² + 10
                      (4x - 10) + 5x = x² + 10
                       4x - 10  =  x² -5x + 10
     
    
0 = x2 – 9x + 20  (liked terms are grouped and simplified)

PROOF:      4x - 10  =  x² -5x + 10
                    4x = x² -5x + 10 + 10
                     0  = x² -5x -4x + 20
                     0  = x² - 9x + 20

Solving:
              x² - 9x + 20 = 0 

              x² - 5x - 4x + 20 = 0

              (x - 5) (x - 4)  = 0

           ⇒ x = 4  (as question says) OR x = 5