problem solving using two variables.

The sum of two integers is 51.
The larger integer is 3 more than twice the smaller 
integer.


Let the larger integer be x
Let the smaller integer bw y

Replace the words "The sum of two integers" by x + y

So now we have 

x + y is 51.
The larger integer is 3 more than twice the smaller 
integer.

Replace "is by an equal sign " = ".

Now we have

x + y = 51.
The larger integer is 3 more than twice the smaller 
integer.

Replace the words "The larger integer" by " x "

Now we have

x + y = 51.
x is 3 more than twice the smaller integer.

Replace the word "is by " = +

x + y = 51.
x = 3 more than twice the smaller integer.

Replace the words "twice the smaller integer" by " 2y ".

Now we have

x + y = 51.
x = 3 more than 2y

To get "3 more than something" write down the "something"
and then add 3 to it.  So we replace "3 more than 2y" by
"2y with 3 added to it", or rather "2y + 3".

x + y = 51
x = 2y + 3

Can you solve that system of equations?  If not post
again.  Answer x = 35, y = 16

That checks because

The sum of 35 and 16 is 51, and
35 is 3 more than 32, which is twice 16.

Edwin