Question

Need Help ASAP
x-y+2z=-2
4x+2y+7z=-9
x+5y+z=-3

Answer 1

There are a few ways to do this. One way is to use substitution.

If you use substitution, then you can solve the first equation `x-y+2z=-2` for x

What do you get when you do this?

Answer 2

how am i able to substitute if none of the varibes are the same?

Answer 3

I'm not sure what you mean by none of the variables being the same?

Answer 4

are you able to solve x-y+2z=-2 for x?

Answer 5

would it be x=-2+y-2z?

Answer 6

yes that's correct

Answer 7

now let's move onto the second equation 4x+2y+7z=-9

Answer 8

We will replace the 'x' with -2+y-2z

to go from

4x+2y+7z=-9

to

4(-2+y-2z)+2y+7z=-9

does this make sense?

Answer 9

yes it does!

Answer 10

now I factor?

Answer 11

so let's do a bit of simplification after replacing x with -2+y-2z

Answer 12

4(-2+y-2z)+2y+7z=-9

4(-2)+4(y)+4(-2z)+2y+7z=-9

-8+4y-8z+2y+7z = -9

-8+4y+2y-8z+7z = -9

-8+6y-z = -9

-8+6y-z+8 = -9+8

6y - z = -1

Do you agree with those steps shown above?

Answer 13

I don't understand how you got -8+6y-=-9

Answer 14

4y+2y = 6y
-8z+7z = -1z = -z

Answer 15

I distributed then combined like terms

Answer 16

wouldn't you subtract though? to set to zero?

Answer 17

I'm not sure what you mean but all I'm doing in those steps is simplifying the left side. When I get to the second to last step, that's when I add 8 to both sides to move the -8 over

Answer 18

only focus on `4(-2+y-2z)+2y+7z`

I turned `4(-2+y-2z)+2y+7z` into `-8+6y-z` through distributing and combining like terms

Answer 19

okay I understand I just am used to subtracting opposed to adding

Answer 20

so you see how I got to 6y - z = -1 ?

Answer 21

yes

Answer 22

now let's move to the equation x+5y+z=-3 (the third given equation at the top)

Answer 23

x+5y+z=-3

-2+y-2z+5y+z=-3 ... replace x with -2+y-2z

what happens when you combine like terms on the left side? What do you get?

Answer 24

-2+6y-1z=-3

Answer 25

good

Answer 26

we can add 2 to both sides to get...

-2+6y-1z=-3

-2+6y-1z+2=-3+2

6y - z = -1

agreed?

Answer 27

agreed c:

Answer 28

So if we replace x with -2+y-2z in equation B, then we end up with 6y - z = -1
if we replace x with -2+y-2z in equation C, then we end up with 6y - z = -1

Essentially this means that this system is `dependent` and there are infinitely many solutions. All of the solutions will fall on the same line

Answer 29

what would y equal?

Answer 30

how does your teacher want you to enter the solution format?

Answer 31

I need the answer for x which we got first off and the answer for y

Answer 32

do you agree how there are infinitely many solutions? is there a special way your teacher wants you to enter the answer? Some teachers will accept "infinite solutions" and you can move on. Other teachers will want you to be more specific

Answer 33

it will depend on what your teacher wants exactly

Answer 34

I honestly have no idea I have to type in what x and y equal the only other option is that there are no solutions. I entered in what we got for x it was incorrect. the answers were in fractions I am beyond confused it said the answer was x=-11/6z-13/6 and y = 1/6z-1/6

Answer 35

I see. Ok so here's how they got y
\[\Large 6y - z = -1\]
\[\Large 6y - z+z = -1+z\]
\[\Large 6y = z-1\]
\[\Large \frac{6y}{6} = \frac{z-1}{6}\]
\[\Large y = \frac{z}{6}-\frac{1}{6}\]
\[\Large y = \frac{1}{6}z-\frac{1}{6}\]
Does this make sense?

Answer 36

honestly no

Answer 37

which step are you stuck on?

Answer 38

ugh I honestly don't know can we try again with different numbers?
ill try and give you my answers as I go?

Answer 39

what I did was add 'z' to both sides first

then I divided both sides by 6 to isolate y. I broke up the fraction to put it in the form your teacher has

Answer 40

sure we can try another one if you want

Answer 41

okay the equation is this
x-y+4z=-4
2x+2y+7x=-9
x+3y+3z=-5

Answer 42

what do you get when you isolate x in x-y+4z=-4 ?

Answer 43

I got y-4z-4

Answer 44

so x = y-4z-4

Answer 45

now we move to equation B which is 2x+2y+7x=-9

we will replace the 'x' with y-4z-4 and simplify things out

2x+2y+7x=-9

2(y-4z-4)+2y+7x=-9

what do you get when you simplify `2(y-4z-4)+2y+7x` ?

Answer 46

yes and I pluged it into the second equation factored and simplified and got -8+4y-z=-9 then added 8 and got 4y-z=-1

Answer 47

wait a moment

Answer 48

you wrote equation B as 2x+2y+7x=-9

is it really supposed to be 2x+2y+7z=-9 ???

Answer 49

yes 7z sorry

Answer 50

ok I agree. I'm getting 4y-z=-1 as well

Answer 51

ready to move onto equation C?

Answer 52

yes I got the exact same solution 4y+-z=-1

Answer 53

ok so equation B and equation C lead to 4y-z = -1

Answer 54

agreed

Answer 55

since we have two identical equations, it leads to `infinite solutions`

Answer 56

I'm assuming your teacher wants you to solve for y here?

Answer 57

correct I need for both y and x