SOLUTION: Solve By The Addition Method ? 2x+y-3z=7 x-2y+3z=1 3x-4y-3z=13

Pick a letter and pick two equations to 
eliminate it from:

I'll pick z and the first and second equations
to eliminate it from:



Just add them term by term as they are and the
z's will cancel out.



Now pick another pair (you have to use one of the
same equations you used before, but make sure
that you use the third one, the one you 
haven't used) and eliminate the SAME letter from
them.

I'll pick the second and third:



Just add them term by term as they are and the
z's will also cancel out.



That equation can be divided through by 2, so we
will go ahead and do that, since it will be
simpler.




So now we have reduced it from three equations in three
variables, to just two equations in two variables:



We will eliminate the y's by multiplying the first equation
through by -3



Add them term by term and get:



Divide both sides by -7





Since that is a terrible fraction, we won't substitute,
but instead go back to 



and eliminate the x's instead:

3x and 2x can both be made into 6x, and so they will
cancel, we multiply the first equation through by 2
and the second ione through by -3 and we get

 

Add them term by term and get:



Divide both sides by 7



That's also a terrible fraction, we could start
all over and eliminate another variable, but
that would just take too long.  So instead we'll just
suffer through substituting the two terrible 
fractions for x and y into one of the original
equations.







We can clear of fractions by multiplying through
by 7:







Divide both sides by 21



My! What terrible fractions those answers are!
But sometimes that's the case.  And those
answers are correct, if you copied the problem
correctly, as



So (x,y,z) = (,,)

Edwin