hello need help with these questions

x + y  = 6     (1)

x = y + 2  subtract y from  both sides ⇒  x - y = 2   (2)

Add (1)  and (2) ⇒   2x  = 8  ⇒   divide both sides by 2 ⇒  x  = 4

Sub this answer  into (1)  [ we could use 2, as well ]

x + y  = 6

4 + y  = 6

So...y   must = 2

(4, 2)

x  = (1/2) y + 5      multiply through by 2 to clear the fraction ⇒  2x  = y + 10    (1)    

2x + 3y  = -14     (2)

Sub (1) into (2)

[ y + 10 ] + 3y  = -14

4y + 10  = -14      subtract 10  from  both  sides

4y = -24    divide through by  4

y  = - 6

Put this into (1) for y ⇒  2x = -6 + 10  ⇒  2x  = 4  ⇒ divide both sides by  2 ⇒  x = 2

So.... ( 2, -6)  is the solution