We have to solve the following system of equations using elimination:

x + y = 6 ...(1)

-x + 7y = 2 ...(2)

First let's eliminate x

Add (1) and (2)

=> 8y = 8

=> y = 1

Now let's eliminate y

7*(1) - (2)

=> 7x + 7y + x - 7y = 42 - 2

=> 8x = 40

=> x = 5

**The solution of the system of equations is x = 5 and y = 1**