Question 572964
I'm going to copy down what you have until I see a problem.

4y+3=3y+x  I started by subtracting ( swinging )
-4y -x -4y -x

You tried doing 2 things at once to save a line of typing - literally - and messed yourself up.


Let me do what you're doing in 2 steps and you'll see:
4y+3=3y+x
-4y  -4y
3 = -y+x
Now subtract x from each side (although I'd have added y to each side so we get rid of those pesky minus signs):
3  =-y+x
-x    -x
3-x = -y  (you had x-2=-1y)
Now I have to multiply both sides by -1 to get y in it's more pleasant positive state :-)
-1(3-x) = -1(-y)
-3+x = y


Now go on with using this in the 2nd equation:
2x+4y=18
2x+4(-3+x)=18
2x-12+4x=18
2x-12= 18
now add 12 to both sides:
6x=30
x=5


So y=-3+x = -3+5 = 2


Checking:
4(2)+3 = 3(2)+5
8+3 = 6+5
11=11 Correct
2(5)+4(2)= 18
10+8=18
18=18 Correct!

Please, don't conserve so much!  Really, think of how much that one line of savings really cost you in time and aggravation tonight.  Write out each step.  You'll have a much better chance, especially on a test, to not miss a step.  The pros do it, so should you.  :-)