Example:

The Cheshire Cat is here to help you
solve this equation by substitution!

Start out with 2 equations like 5x-3y=18
and 4x-6y=0.

Solve either of the 2 equations for either of 
the 2 variables.  I will solve 5x+3y=18
for y.

 
5x-3y=18
subtract the 5x from both sides.
-3y=18-5x
divide both sides by -3.
you are now left with
 y=-6+5/3x.

 
4x-6(-6+5/3x)=0

Solve now for the variable x.

4x-6(-6+5/3x)=0
multiply the -6 to the -6 and the 5/3x
4x+36-10x=0
add like variables and subtract the 36
from both sides.
-6x=-36
now divide both sides by -6
x=6
 

You now have the answer for the x of the
ordered pair.  You now need the y.  Do this
by substituting the x=6 into either of
the equations.  I will replace the x in
5x-3y=18.

5x-3y=18
replace the x with 6
5(6)-3y=18
multiply the 5 and 6
30-3y=18
subtract 30 from both sides
-3y=-12
divide both sides by -3
y=4