Expert: Abe Mantell - 1/12/2005

Question
I am having trouble understanding how to solve linear equations by using the elimination method. I don't understand how to choose the numbers you multiply the equations by an di am having trouble undersatnding how to solve the equation after that. The substitution method is easy, but the elimination method is still sort of foggy to me. I am in 8th grade, Algebra 1
Thank you for your help.

Answer
Hello Reilly,

We make the selection based upon which variables we
select to eliminate and what the least common multiple
is of their cofficients.

For example:
2x-3y=8
6x-4y=7

Let's select the x's to eliminate...so, we see the
LCM of 2 and 6 (the coefficients of x) is 6.  Thus,
we need to multiply the 1st equation by 3 and leave
the second equation as is...actually it would be better
to multiply by -1 so when we add the two equations we
get the elimination we want!  Thus, we get:
6x-9y=24, and
-6x+4y=-7...now add them!
to get: -5y=17 ==> y=-17/5

Now we can redo this to eliminate the y's...or just
substitute y=-17/5 into one of the equations and
solve x.

OK?

Abe