Given,

x + y = 10 ..............1

x - y = 2 .................2

Add equation 1 and 2, we get

      x + y + x - y = 10 + 2

=> 2x = 12

=> x = 12/2

=> x = 6

Put value of x in equation 1, we get

     6 + y = 10

=> y = 10 - 6

=> y = 4

So, system of linear equation has solution: x = 6 and y = 4