1. ## three variables

What I am doing wrong here?

Also does it matter that there are only two variables in the third line? All the examples I have looked at for solving three equations with three variables had three variables in each line.

2x + y + z = 21
2y + x + z = 20
2x + 2y = 22

define x

x + y = 11
x = y -11

substitute into line 1 and 2:

2(11 - y) + y + z = 21
22 - 2y + y + z = 21
22 + z = 21 + y
z = y - 1

2y + (y-11) + z = 20
3y - 11 + z = 20
3y + z = 31

substitute again:

3y + (y-1) = 31
4y = 32
y = 8

thanks!

2. i would suggest elimanating the z in eq1 and eq2
and factor out 2 in the eq3

this will make it very easy

you should get

x=6
y=5
z=4

3. Sorry, I don't follow. You would need to explain it a bit further.

Also, I would really like to know why my method doesn't work, and if the lack of three variables in the third line is an issue.

thanks

4. your method probably works but substituting in equations into equations gets very difficult and error prone, you want reduce the equations down to very simple terms

so the first 2 equations are

2x+y+z=21
2y+x+z=20 (multiply thru with -1 and re oder the terms)

so now we have

2x+y+z=21
-x-2y-z=-20

x - y = 1

now take eq3 factor out 2 you have

x + y = 11

now add these equations together and we have

x=6

y and z are very easy to get from here

did you see the magic??

5. Yes I see.

But is that method only possible because of the third line in this case?

2x + y + z = 72
2y + x + z = 64
2z + x + y = 68

x - y = 8

then I would have to follow my original method of substitution, no?

Sorry, I'm just trying to figure out how the proper method for doing these.

6. Originally Posted by aquajam
define x

x + y = 11
x = y -11
it should be $x = 11 - y$

7. ^^
That's what I thought at first, and I tried what you suggested. I must have made a mistake somewhere, I'll try again.

8. not necessarily
with 3 variables in 3 equations
try to eliminate one of variables first
it doesn't mater which one just pick the easy one first
often you can eliminate 2 variables in one sweep
again try avoid plugging in an equation into an equation with simultaneous equations
there are times when there is no choice.. but don't see it here.

the next simultaneous equation can be very easy by just eliminating the z

not questioning your method.... but it takes more steps
my view anyway.

9. Okay, I see my mistake in the first one.

I had I should have used (11-y) in the second substitution. Had it right in the first one.

I also see your point about being eliminate variables more simply. It's just all the tutorials I've looked at, suggested the longer way.