SOLUTION: I am confused on how you go about solving this substitution problem 4y+3=3y+x 2x+4y=18 I started to try doing this problem several different ways but I'm not sure how to so

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Question 572964: I am confused on how you go about solving this substitution problem
4y+3=3y+x
2x+4y=18
I started to try doing this problem several different ways but I'm not sure how to solve it. Here's how I attempted to do it.
4y+3=3y+x I started by subtracting ( swinging )
-4y -x -4y -x
= x-2=-1y
+2 +2
-1/2x -1=y
2x+4=18
2x+4( -1/2x-1)=18
2x+ -2x -4=18
0x-4=18
+4 +4
0x=22
Divide by 0 on each side.
X=0
-1/2(0)-1
(0,1)
Found 2 solutions by mathsmiles, solver91311:
Answer by mathsmiles(68) (Show Source):
You can put this solution on YOUR website!
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. :-)

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

I'm not sure what you did wrong exactly because the rendering of your work just doesn't line up so that it is understandable. But let me show you where you should have been following your line of reasoning.

Add and to both sides:

Multiply by -1

Now substitute for in the second equation:

Solve for , then substitute back into either original equation and solve for .

And NEVER, NEVER, NEVER again even THINK about dividing ANYTHING by zero.

John

My calculator said it, I believe it, that settles it