Let's actually find the solution of
2x - 6y = 8
-x + 3y = 10
Let's use the addition/subtraction method. Multiply the 2nd equation by 2, obtaining
2x - 6y = 8
-2x + 6y = 20
--------------------
0 + 0 = 28
Since this can never be true, the system of linear equations
2x - 6y = 8
-x + 3y = 10
has no solution.
