Question

Solve the system using any algebraic method. (I used matrices and I got 0,0,1??!! Medal & fan for help!!
x+2y+3z=5
3y-4z=-9
x=-2z

Answer 1

Is that the Equation?

Answer 2

yes

Answer 3

Mk.

Answer 4

Let's solve for x.
x+2y+3z=5
Step 1: Add -2y to both sides.
x+2y+3z+−2y=5+−2y
x+3z=−2y+5
Step 2: Add -3z to both sides.
x+3z+−3z=−2y+5+−3z
x=−2y−3z+5

Answer 5

ok

Answer 6

Did that help?

Answer 7

Let me try solving it first...

Answer 8

I got 5, -1.59, 1.06. It looks about right
I rounded it to the nearest hundreths

Answer 9

\[\large x + 2y + 3z = 5\]
\[\large 3y - 4z = -9\]
\[\large x = -2z\]

We can solve that second equation for 'y' and substitute it into the first equation

\[\large 3y - 4z = -9 \rightarrow y = \frac{-9 + 4z}{3}\]

Replace that in the first as well as replace 'x' with -2z *from the third equation*

\[\large x + 2y + 3z = 5 \rightarrow -2z + 2(\frac{-9 + 4z}{3}) + 3z = 5\]

\[\large -2z + \frac{-18 + 8z}{3} + 3z = 5\]
\[\large -6z -18 + 8z + 9z = 15\]
\[\large 11z = 33\]
\[\large z = \frac{33}{11} = 3\]

From there...you can solve for 'x'...and then for 'y'

Answer 10

Thank you sir!

Answer 11

No problem, but let me know if anything doesnt make sense!

Answer 12

Wait, I try pluggin in the numbers but it doesn't match up

Answer 13

Do you mind pluggin it in for me pls?

Answer 14

Well what do you get for the numbers? z = 3...what do you get for x and y?

Answer 15

x=-6 and y=5?

Answer 16

My 'x' matches but not 'y'

Lets see...

Answer 17

ok

Answer 18

Good Job, Jasmine.

Answer 19

Thank you!

Answer 20

So just take any of the equations...like the first one

\[\large x + 2y + 3z = 5\]
\[\large -6 + 2y + 3(3) = 5\]
\[\large -6 + 2y + 9 = 5\]
\[\large 3 + 2y = 5\]
\[\large 2y = 5 - 3\]
\[\large 2y = 2\]
\[\large y = 1\]

Answer 21

You Are Welcome!

Answer 22

Thx @johnweldon1993. I see where I messed up

Answer 23

Not a problem :)

Answer 24

Can u pls help me with the others too?

Answer 25

I can't close my current problem so i am just going to post it here.
-4x-y+5z=-7
2y+18z=0
2x+y+2z=5

Answer 26

Mk. i will help you.

Answer 27

Thanks :)

Answer 28

No Problem.

Answer 29

@braydenbunner

Answer 30

Help pls

Answer 31

Oh sorry didnt realize you posted back lol

Answer 32

it's totally fine!

Answer 33

So, Whats your next question?

Answer 34

I can't close my current problem so i am just going to post it here.
-4x-y+5z=-7
2y+18z=0
2x+y+2z=5

Answer 35

That is ok.

Answer 36

Ok for the first one. What are you solving for X or Y?

Answer 37

i think y?

Answer 38

Alright Well.
Let's solve for y.
−4x−y+5z=−7
Step 1: Add 4x to both sides.
−4x−y+5z+4x=−7+4x
−y+5z=4x−7
Step 2: Add -5z to both sides.
−y+5z+−5z=4x−7+−5z
−y=4x−5z−7
Step 3: Divide both sides by -1.
−y
−1
=
4x−5z−7
−1
y=−4x+5z+7

Answer 39

ok

Answer 40

can i see it with x

Answer 41

You'll find the answer to this one quick :)

Answer 42

Ok.

Answer 43

ok, but i am struggling..

Answer 44

\[\large -4x-y+5z=-7\]
\[\large 2y+18z=0\]
\[\large 2x+y+2z=5\]

Lets add the first and third equations..it will eliminate the 'y'

\[\large -4x - y + 5z = -7\]
\[\large +(2x + y + 2x = 5)\]

Gives us

\[\large -2x + 7z = -2\]


Now we only have 2 equations to work with...

\[\large -2x + 7z = -2\]
and
\[\large 2y + 18z = 0\]

What do you notice about these 2 equations?

Answer 45

Let's solve for x.
−4x−y+5z=−7
Step 1: Add y to both sides.
−4x−y+5z+y=−7+y
−4x+5z=y−7
Step 2: Add -5z to both sides.
−4x+5z+−5z=y−7+−5z
−4x=y−5z−7
Step 3: Divide both sides by -4.
−4x
−4
=
y−5z−7
−4
x=
−1
4
y+
5
4
z+
7
4

Answer 46

one of them is lacking a x and y. also the both have a z

Answer 47

Well even more general....in total with 2 equations...we have 3 different unknowns we have to solve for

And how could we POSSIBLY solve 3 unknowns with only 2 equations...we cannot

This system of equations has no solution

Answer 48

oh ok. no wonder why i couldn't solve it

Answer 49

so would i just put no solution?

Answer 50

Yeah, no solution :)

Answer 51

thanks @johnweldon1993

Answer 52

Thank you johnweldon1993. Much Thanks

Answer 53

yes

Answer 54

omg my computer is being slow

Answer 55

I have more that I need help with
-x-y-2z=9
-2x-2y-z=-1
-z-y+z=-10

Answer 56

ooops i meant 1 not =-1

Answer 57

-x-y-2z=9
-2x-2y-z=1
-z-y+z=-10

Answer 58

Is that third equation correct?

Answer 59

oops it's wrong. it is suppose to be -x

Answer 60

Damn I was gonna say this got a whole lot easier lol

Answer 61

lol

Answer 62

It gets easier as you go along and learn the steps.

Answer 63

ok

Answer 64

@johnweldon1993 pls help

Answer 65

What do you need help with?

Answer 66

with that. I need explanations.

Answer 67

Mk.

Answer 68

Let's solve for x.
−2x−2y−z=1
Step 1: Add 2y to both sides.
−2x−2y−z+2y=1+2y
−2x−z=2y+1
Step 2: Add z to both sides.
−2x−z+z=2y+1+z
−2x=2y+z+1
Step 3: Divide both sides by -2.
−2x
−2
=
2y+z+1
−2
x=−y+
−1
2
z+
−1
2

Answer 69

i typd it up while i was sitting here.

Answer 70

ok so x=2

Answer 71

Yep Good Job! :)

Answer 72

thanks! can you help show me how you solve for y and z too pls?

Answer 73

Sure.

Answer 74

Let's solve for z.
−2x−2y−z=1
Step 1: Add 2x to both sides.
−2x−2y−z+2x=1+2x
−2y−z=2x+1
Step 2: Add 2y to both sides.
−2y−z+2y=2x+1+2y
−z=2x+2y+1
Step 3: Divide both sides by -1.
−z
−1
=
2x+2y+1
−1
z=−2x−2y−1

Answer 75

Thanks!

Answer 76

Not to interrupt *And sorry I was away*

I'm not getting a solution here...I'm gonna check it again but

Answer 77

It's totally fine. Ok

Answer 78

Let's solve for y.
−2x−2y−z=1
Step 1: Add 2x to both sides.
−2x−2y−z+2x=1+2x
−2y−z=2x+1
Step 2: Add z to both sides.
−2y−z+z=2x+1+z
−2y=2x+z+1
Step 3: Divide both sides by -2.
−2y
−2
=
2x+z+1
−2
y=−x+
−1
2
z+
−1
2

Answer 79

so y=2?

Answer 80

Yes Good Job!! :)

Answer 81

Thx. can u pls show me how to solve for z

Answer 82

Sure thing.

Answer 83

Let's solve for z.
−2x−2y−z=1
Step 1: Add 2x to both sides.
−2x−2y−z+2x=1+2x
−2y−z=2x+1
Step 2: Add 2y to both sides.
−2y−z+2y=2x+1+2y
−z=2x+2y+1
Step 3: Divide both sides by -1.
−z
−1
=
2x+2y+1
−1
z=−2x−2y−1

Answer 84

The answers don't match up quite well

Answer 85

I know.

Answer 86

@Directrix pls help me

Answer 87

Its the number that is the answer. If you get it wrong let me know and i will Explain it in another way.

Answer 88

here can you try plugin in the variables.

Answer 89

i want to see if i mess up somewhere

Answer 90

Mk

Answer 91

@pooja195 pls help, I am struggling.

Answer 92

@pooja195 Ma'am Is it ok if you help this young lady?

Answer 93

@satellite73 pls help

Answer 94

It seams they are offline :/.

Answer 95

yea

Answer 96

Do you have anymore?

Answer 97

yea