`2x+6y=16`

`2x-3y=7`

Write the system of equations as an augmented matrix.

`[[2,6|16],[2,-3|7]]`

Multiply the second line by -1.

`[[2,6|16],[-2,3|-7]]`

Eliminate the first column.

`[[2,6|16],[0,9|9]]`

`9y=9`

`y=1`

`2x+6y=16`

`2x+6(1)=16`

`2x=10`

`x=5`

The solution set is (5, 1).