#1**+1 **

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

CPhill Aug 14, 2018