Question

systems with 3 variables, solve by substitution:
x+5y-4z=-10
2x-y+5z=-9
2x-10y-5z=0
there is answer choices as well, I have been trying to work this out for about 2 hours now and I cannot think of anything else to try! please help!!!!

Answer 1

hi insanity cat :)

Answer 2

srry bethany

Answer 3

you can use substitution to find the value of one variable
we can find the value of x in the first variable easily
x=-10+4z-5y
and hello there

Answer 4

haha its okay!

Answer 5

bai i dont know to solve those problems....

Answer 6

im still confused!! :/ the steps that I have were making since but it just never gave me the x, y, and z

Answer 7

so lets substitute x
2x-y+5z=-9 2x-10y-5z=0
2(-10+4z-5y)-y+5z=-9 2(-10+4z-5y)-10y-5z=0
-20+8z-10y-y+5z=-9 -20+8z-10y-10y-5z=0
-11y+13z-20=-9 -10y+3z-20=0
-11y+13z=11 -10y+3z=20

Answer 8

so x would be 20? .... wait no, because that's not an answer choice. its either 5, or -5 for x

Answer 9

but I don't see how I would get either one!

Answer 10

well if you plug the equation into a calculator with the capabilities to solve a system like this you get x=-1 y=-1 and z=0

Answer 11

sorry x=-5

Answer 12

what kind of calculator are you using?? lol I need it!

Answer 13

insanity, for the second equation after substitution you have -10y-10y = -20y , not -10y

Answer 14

I have a TI-nspire with me

Answer 15

i was just going to check over taht

Answer 16

that*

Answer 17

So bethany, have you followed up to the substitution part from @insanitycat 's method?

Answer 18

2x-y+5z=-9 2x-10y-5z=0
2(-10+4z-5y)-y+5z=-9 2(-10+4z-5y)-10y-5z=0
-20+8z-10y-y+5z=-9 -20+8z-10y-10y-5z=0
-11y+13z-20=-9 -20y+3z-20=0
-11y+13z=11 -20y+3z=20

Answer 19

Good.

Answer 20

so you substitute the first equation into the second for x, right?

Answer 21

for the second and third.

Answer 22

no you can get x from the first equation and then substitute the x-value into the 2nd and third

Answer 23

I still don't see where -5 would come in for x

Answer 24

we will get to that

Answer 25

first we need to find y and z

Answer 26

this uses the elimination method

Answer 27

this kind of substitution would require elimination though in order to make it a two variable equation

Answer 28

no it is supposed to be elimination

Answer 29

Ah... at top you stated substitution.

Answer 30

so we substitute y=-1 into one of the equations to find z
-11y+13z=11
-11(-1)+13z=11
13z+11=11
13z=0
z=0

Answer 31

I typed it wrong... but I was getting the part where it becomes 2 problems wrong so you can solve it as two equations!

Answer 32

There you go, now you've got y=-1 and z = 0, do you understand how you achieved both of these values?

Answer 33

the next prob is substitution, this one is elimination! sorry yall

Answer 34

then we can substitute both the y and z values into the equation for x now
x=-10+4z-5y
x=-10+4(0)-5(-1)
x=-10+5
x=-5

Answer 35

Thank you @insanitycat and @bethanyquintero good luck!

Answer 36

ok wait, I understand everything on how to work the problem, but how you got -1 for x...

Answer 37

x = -5, y=-1.

Answer 38

x=-5

Answer 39

i see it now, so i see how to get the x and z but how did you get the y=-1..... if i can get that then i will completely understand the problem!