Question

I have to solve using elimination.
x + y -2z = 8
5x - 3y + z = -6
-2x - y + 4z = -13

I think I'm doing it right, so far I've got
-5(x + y -2z = 8)
-5x - 5y + 10z = 8
5x - 3y + z = -6
_____________________
-8y + 11z = -46

from there, do I isolate y and then substitute the y into the other equation or?

Answer 1

Have you heard of Gaussian elimination?

Answer 2

No?

Answer 3

I would multiply the first equation, by 2 and then add it to the last equation.

Answer 4

then you get y=3

Answer 5

So it would be
2(x + y -2z = 8)
2x + 2y -4z = 16
-2x - y + 4z = -13

Answer 6

yeah

Answer 7

so it cancels out both the x and z variables making it
y=3?

Answer 8

then I can substitute that into the the first equation right?

Answer 9

yes, now plug that into the first two equations

Answer 10

then you have x-2z=5 and 5x+z=3

can you solve this system of two equations with two variables?

Answer 11

I think I can, let me try it out on paper if that's ok

Answer 12

I did
x + 3 -2z = 8
-2x - 3 + 4z = -13
____________________
-x + 2z = -5
-x = -2z - 5
x = 2z + 5

Answer 13

but then I did
x + y -2z = 8
2z + 5 + 3 - 2z = 8

the z's cancel each other out so I think I did something wrong or it doesn't have a solution?

Answer 14

no it does, if you take y=3 and plug into the first two equations, you get
x-2z=5 and 5x+z=3

multiply the first one by -5
-5x+10z=-25
and we have the other one
5x+z=3

add them

11z=-22
z=-2

Answer 15

now solve and get x=1, y=3, z=-2

Answer 16

If you're interested, check out matrices-specifically the coefficient matrix- on khanacademy, you'll notice it is exactly what you are doing, but with less writing!

Answer 17

yeah I mentioned Gaussian elimination at the top but if he didn't know about it I am guessing they should not use it. But it is much nicer...

Answer 18

you kind of lost me when you got
x-2z=5 and 5x+z=3

when I substituted, I got
x + 3 - 2z = 8 and 5 -9 + z

Answer 19

@FibonacciChick666 mentioned matrices, but we skipped that in the book

Answer 20

they should really teach matrices instead of this crap. @fluttere, if you don't mind looking, gaussian elimination is worth learning

Answer 21

@fluttere lol

Answer 22

....really? It won't let me tag your name

Answer 23

where I lost you

plug in y=3 to the first equation and simplify x+y-2z=8 becomes x+3-2z=8 becomes
x-2z=5

do the same thing for the second equation, plug in y=3
5x - 3y + z = -6
becomes
5x-9+z=-6
5x+z=3

so we have
x-2z=5
5x+z=3

Answer 24

now solve that, and get the two answers for x and z, and we know y=3

Answer 25

Go read about matrix elimination method. It is the exact same thing in different notation, and you will be surprised how much the notation makes it easier to see.