I can't answer x+3y=6 right now.  I have two variables (x and Y) so I'm stuck.

So, I turn to my other equation.  y-3=7.  If I add three to each side of the equation, I get y=10.

Now that I know y=10, I can put the number 10 in every place there was a "y."  So, the second equation looks like this...

x+3y=6

x+3(10)=6

x+30=6      So I subtract 30 from each side.

x=-24

I then check myself by putting all my numbers back into the original equations.

10-3=7 and -24+3(10)=6

Yep, that works.