Question 12985
There are several ways to do this.  The elimination method usually works well when the equations are both in standard form, as in this case.  

x - 4y = -2
x + 2y = 4 


In order to eliminate the x variable, multiply the first equation by -1, and rewrite the second equation as it is:

-x + 4y = 2
x + 2y = 4


Now add these two equations together giving you

6y = 6
y=1


Substitute the y = 1 back into either equation, say the first one:

x - 4y = -2
x - 4(1) = -2
x-4 = -2


Add 4 to each side:
x-4+4 = -2 + 4
x=2


Check in the second equation, by letting x= 2 and y = 1:
x + 2y = 4 
2 + 2(1) = 4
It checks!


R^2 at SCC