Math Forum / Mathematics / Recreational Math / December 2005

You haven't told us what you are trying to do with these equations.
Assuming that you are trying to solve them by elimination, the idea is
to multiply by whatever it takes to get one of the variables to have
the same coefficient in both equations. Then when you subtract them
(or add them if the signs are opposite) you will have only one
variable left in the resulting equation, thus "eliminating" one
variable. In your above example your equations would both have a 10x
after your multiplication, so subtracting will give a pure y equation.

If the bottom equation were 3x + y so your system is:

2x + 3y = 1700
3x + y = 2600

you might just multiply the second equation by 3 making the y terms
the same. What you do depends on the equations you have.

--Lynn