x = 16/7, y = -6/7
For elimination I will multiply the first equation by -3 to get the x to cancel
x - 2y = 4 --> -3x + 6y = -12
Now we bring back the other equation and treat it like an addition problem:
-3x + 6y = -12
3x + y = 6
+———————
7y = -6
y = -6/7
To get x we will use this y-value and plug it into one of the equations:
3x + y = 6,
3x + (-6/7) = 6
3x - 6/7 = 6
3x = 48/7
x = 16/7
So the solution is x = 16/7, y = -6/7, and if you are ever unsure you can put both of these values into both system of equations to see if the equations are true.