Question

Solve the system by elimination
{ x+y-2z=8
{5x-3y+z=-6
{-2x-y+4z=-13

Answer 1

x+y-2z=8
-2x-y+4z=-13... Cancel out the y's.
((((-x+2z=-5))))... new equation with 2 variables

using eq 1 and 2... lets eliminate the y's
x+y-2z=8
5x-3y+z=-6... notice that to eliminate the y's we need to multiply eq #1 times 3
so we get:
3x+3y-6z=24
5x-3y+z=-6... cancel y's out and:
((((8x-5z=18))))... equation with two variables # 2

Answer 2

now we have a system of two equations with two variables:
-x+2z=-5
8x-5z=18... can you solve for one of the variables?

Answer 3

let me see

Answer 4

not sure

Answer 5

if you multiply equation #1 by 8 you can cancel the x's out... give it a try

Answer 6

ok

Answer 7

equation one is -x+2z=-5 right

Answer 8

yes

Answer 9

-8x+16z=-40?

Answer 10

right ;)

Answer 11

now you can cancel -8x with 8x and add up the rest... try it

Answer 12

wait wouldn't z cancel out as well?

Answer 13

or would it be negative z instead of minus

Answer 14

you will get -8x+16z=-40
8x-5z = 18.... x's cancel out.... z's do not cancel out only x's
add up and you get 11z=-22
z=-22/11
z=-2

Answer 15

we know one variable out of three, we still need two more ;)

Answer 16

ok do I put in z in the original equations now to find the other variables?

Answer 17

that's right....I would use -x+2z=-5, it looks easier

Answer 18

plug in and solve for x ;)

Answer 19

-x+-4z=-5?

Answer 20

sorry not -4z but -4

Answer 21

yes... now solve for x :P

Answer 22

x=1?

Answer 23

x=1 :)

Answer 24

we have one more to go

Answer 25

ok

Answer 26

now we can go back to the very first equation and plug in the values for z and for x to solve for our y... try it ;)

Answer 27

x+y-2z=8 use this one since it looks simple ;)

Answer 28

um 1+y-(-4)=8?

Answer 29

not sure what y would equal

Answer 30

first plug in:
(1)+y-2(-2)=8
(1)+y+4=8
y=8-4-1
y=3

Answer 31

now to prove that this is right:
plug in all the values for x,y,z in equation #3 that you were given first, if you get -13 then it is right :P

Answer 32

what do u get? :P