x-y=2 and x+y=8

Solve the following system:
{x-y = 2 |     (equation 1)
x+y = 8 |     (equation 2)
Subtract equation 1 from equation 2:
{x-y = 2 |     (equation 1)
0 x+2 y = 6 |     (equation 2)
Divide equation 2 by 2:
{x-y = 2 |     (equation 1)
0 x+y = 3 |     (equation 2)
Add equation 2 to equation 1:
{x+0 y = 5 |     (equation 1)
0 x+y = 3 |     (equation 2)
Collect results:

Answer: x=5        y=3
 

x-y=2 ----(1)

x+y=8 ---- (2)

(1)+(2): 2x=10

x=5----- (3)

Subst. (3) into (1)

5-y=2

y=3

Therefore x=5 and y=3