Question

solve the system by elimination
please help not sure how to do this

Answer 1

-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5

Answer 2

Add equation 1 and 3 and then 2 and 3. The x terms are eliminated, leaving two equations in two unknowns, y and z.

Answer 3

The sum of equations 1 and 3 is: 5y+6z=5
The sum of equations 2 and 3 is: 2y+4z=-3

Answer 4

Now solve the remaining equations for y and z.
Plug in the solutions for y and z into any of the equations and then solve for the result for x.

Answer 5

solve the result for x. sorry.

Answer 6

I make a mistake in one of the calculations above, sorry. That is what can happen when an 82 year old engages in mental calculations.
Have bail out now.
For your information the solutions are: {x = 1, y = 1, z = 0}

Answer 7

Can even write correct English at this moment.
Bye.

Answer 8

Hello!

You want to solve this system of linear equations:

-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5

Let's (arbitrarily) elimiinate x first, leaving us with a system in y and z.

Add the first and third equations together. What do you get?

Add the 2nd and 3rd equations together. What do you get?

Answer 9

5y+6z=5
2y+4z=-3

Answer 10

Plese check that -3. Where did -3 come from?

Answer 11

i just brought it down

Answer 12

Again, add the 2nd and the 3rd equations together. What do you get for your constant on the right side of your result?

Answer 13

would it be 2?

Answer 14

yes.
Write out your 2 new equations. Note that x has disappeared, as we wanted it to.

Answer 15

so 5y+6z=5
and 2y+4z=2

Answer 16

very good. Now, we arbitrarily choose to eliminate y. (we could choose to eliminate z if we wanted to).

Divide the entire 2nd equation by 2 now, please. Your result?

Answer 17

im confused how do i do that

Answer 18

Your 2nd equation is 2y + 4z = 2
Div it by 2: ----------- = y + ? = ?
2

Answer 19

y+2z=1

Answer 20

Yes. now, we want to eliminate y and find z.

first equation is 5y + 6z = 5

Please mult your new 2nd equation by -5 and write the result immediately below
your first equation (5y + 6z = 5).

Answer 21

Awaiting your response.

Answer 22

like i said im sloowly getting confused

Answer 23

first equation is 5y + 10z = 5. After you mult. the 2nd equation by -5, you get
-5y -6z = -5

Please add these two equations together. 5y-5y=0 (and so on).

Answer 24

so add 5y-5y=0 and -5y-6z=-5?

Answer 25

Combine (or "add") 5y + 10z = 5
and -5y-6z =-5

Answer 26

so y+4z=0

Answer 27

but 5y-5y=0. Try again, pls

Answer 28

what? you said 5y+10z=5 and -5y-6z=-5

Answer 29

Indeed I did say that. What's not clear for you?

Answer 30

5y
-5y
-----
0

Answer 31

You should get 4z=0. Solve that for z, please.

Answer 32

z=4?

Answer 33

but 4z=0, and if we divide both sides by 4, we get z=0.

Answer 34

oh okay

Answer 35

soo z=0

Answer 36

yes, indeed.

Answer 37

Now we have to find y and x.

Answer 38

Any idea of how to do that?

Answer 39

do i plug in 0 for x?

Answer 40

You could go back to the original 3 equations and plug in 0 for z (not for x).

would you do that now, please?

Answer 41

which one do i plug it in for

Answer 42

Please go back to ALL 3 of the original equations. Let z=0 in each and every one.

What 3 equations do you get?

Answer 43

oh so do it for all 3 of them
give me a min

Answer 44

Yes, all three of :

-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5

plug in 0 for z in 3 different places.

What's left is

-2x+2y+ 0 =0
-2x-y =-3
2x+3y =5

Answer 45

We want to find x and y.

Add the last 2 equations together. Your result?

Answer 46

-2x+2y+3(0)=0
-2x-y+0=-3
2x+3y+3(0)=5

Answer 47

Very good. Add the last 2 equations together now.

Answer 48

so x+2y+0=2

Answer 49

Addition error. Note that 2x-2x = 0. You are just subtracting 2 from 2 (wrong); subtract 2x from 2x. Try again.

Answer 50

2x-2x=0

Answer 51

Tghat's correct, but I had asked you to add together (combine) the last 2 equations.

Answer 52

oh so 2x+2x=4x

Answer 53

-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5

becomes

-2x+2y =0
-2x-y =-3
2x+3y =5

Add the last 2 equations together now.

Answer 54

Note that -2x+2x=0.

Answer 55

yes that is what i said above

Answer 56

So you should have obtained 0x + 2y = 2 (not 0).

Answer 57

Solve 2y = 2 for y, please.

Answer 58

2y/2=2/2
y=1

Answer 59

Yes. Now, z=0, y=1. How would you find the value of x?

Answer 60

now sure

Answer 61

go back to the original 3 equations. Pick any one of those three. type your choice below.

Answer 62

2x+3y+3z=5

Answer 63

Now let y=1 and z=0. What do you get?

Answer 64

so 2x+3(1)+3(0)=5

Answer 65

2x+3+0=5

Answer 66

Indeed. simplify that. find the value of x.

Answer 67

3+0=3
2x+3=5

Answer 68

2x+3-3=5-3

Answer 69

You must solve for x.

2x+3=5. Find x.

Answer 70

2x=2
x=1

Answer 71

correct. x=1, y=1, z=0

Go back to the beginning and pick another (different) equation. Your choice.

Answer 72

-2x+2y+3z=0

Answer 73

now let x=1, y=1 and z=0. What happens?

Answer 74

so -2(1)+2(1)+3(0)=0

Answer 75

what is -2+2?

Answer 76

0

Answer 77

what is 0+3(0)?

Answer 78

0

Answer 79

So, has your equation become true or not? 0=0??

Answer 80

true

Answer 81

So we have solved this system of linear equations. using the method of elimination. Any questions?

Answer 82

wow thank you so much for you help i really appreciate it thank you so much!!!:)

Answer 83

My pleasure!! Feels so nice to be appreciated. Good luck! See you again.

Answer 84

Hope your Song of the Soul is sweet music.

Answer 85

ab-soul-ty is

Answer 86

:)