What is the balance method solution of 3y+7=35-4y?

You have to keep the equation balanced.  Whatever you do to one side you have to do to the otherside as well.

In this picture, you would want to get the x by itself, but to do so you need to take away 10 from the left hand side,  that's okay but if you want the scale to stay balanced then you have to take 10 off the other side as well.

I just got a pop up showing me that Rosala has answered your question so I will see what she has written.

You don't need two great answers lol.

no I think I will show you more.

$$\begin{array}{rlll}
3y+7&=&35-4y\qquad &\mbox{}\\\\
3y+7+4y&=&35-4y+4y\qquad &\mbox{Add 4y to both sides}\\\\
7y+7&=&35\qquad &\mbox{Simplify both sides}\\\\
7y&=&28\qquad &\mbox{subtract 7 from both sides}\\\\
7y\div 7&=&28\div 7\qquad &\mbox{divide both sides by 7}\\\\
y&=&4\qquad &\mbox{Simplify both sides}\\\\
\end{array}$$

So we'll solve this like this:

$$3y + 7 = 35 - 4y$$  (now we'll change the places of the values and put them in their suitable places)

$$3y + 4y = 35 - 7$$

$$7y=28$$ (now we'll take 7 to the other side)

$$y=28/7$$ (now we'll simply devide 28 and 7 which then will give us our y)

$$y=4$$  $$ANSWER$$

I hope now that uve understood by now but if not then pls be free to ask!

I hope this helps!