Question

Solve the following system. Show all your work.
3x-2y+2z=30
-x+3y-4z=-33
2x-4y+3z=42

Please help me I really need your help can you tell me how to do it too I dont get it... I need it ASAP

Answer 1

x

Answer 2

Thank you soo much

Answer 3

You can use elimination to eliminate one variable.
Then you will have a system of 2 equations with 2 unknowns to solve.

Answer 4

Look at equations 1 and 2. Can you eliminate x?

Answer 5

yes 2x

Answer 6

Okay let me do that real quick

Answer 7

No. 2x is not eliminating x.
Equation 1 has 3x.
Equation 2 has -x.
Ok so far?

Answer 8

2x+y-2z-3

Answer 9

Is what you get when you eliminate am I correct?

Answer 10

If you multiply equation 2 by 3, you will have -3x. Then when you add the new equation 2 to equation 1, x will be eliminated.

Answer 11

Oh multiply
K

Answer 12

Each time you add equations, you need to eliminate a variable.

Answer 13

I really dont understand this..

Answer 14

And I pay attention in class 2...

Answer 15

It is just soo confusing

Answer 16

We'll do it step by step.

Here are the two equations 1 and 2 in their original form.
Eq.1 3x-2y+2z=30
Eq. 2 -x+3y-4z=-33

Answer 17

Now we keep equation 1 as is and we multioply the entire equation 2 by 3, and write it below eq. 1.

Answer 18

Oh by 3
Okay

Answer 19

Eq.1 3x - 2y + 2z = 30
New Eq. 2 -3x + 9y - 12z= -99

Answer 20

Now we add them together. Notice, the x terms cancel out.

Answer 21

Yes so the equation afterwards will be 7y -10z=-69

Answer 22

Eq.1 3x - 2y + 2z = 30
New Eq. 2 -3x + 9y - 12z= -99
--------------------------------
add 7y - 10z = -69

Answer 23

Correct.

Answer 24

Now we need to pick a different pair of equations and again eliminate x.

Answer 25

Let's use equations 2 and 3.

Answer 26

Okay

Answer 27

Eq. 2 -x+3y-4z=-33
Eq. 3 2x-4y+3z=42

By multiplying Eq. 2 by 2, the x's will be eliminated after adding the two eqs togeher.

Answer 28

so it will be -y-z=9

Answer 29

You must multiply the entire eq 2 by 2.

New Eq. 2 -2x + 6y - 8z = -66
Eq. 3 2x - 4y + 3z = 42
------------------------------
add 2y - 5z = -24

Answer 30

Oh okay

Answer 31

And than after that you get both of the answers that you simplified and and them together

Answer 32

So 7y-10z=-69
2y-5z =-24

Answer 33

Now take the two equations with x eliminated, and you have a system of 2 equations in 2 unknowns.

Answer 34

Correct.
Since we are already using elimination, let's continue with that method.

7y - 10z = -69
2y - 5z = -24

Look at -10z and -5z. If we multiply the seciond eq by -2, the z term will become 10z which when added to -10z of the eq above will eliminate z.

Answer 35

This is the part I dont get...

Answer 36

We are using elimination to solve a system of 2 equations n 2 unknowns.

Keep eq. as is 7y - 10z = -69
Multiplied by -2 -4y + 10z = 48
-------------------
add 3y = -21
y = -7

Answer 37

So you multiplied the bottom equation by -2 correct?

Answer 38

yes

Answer 39

And what do I do after that
I found y but after that do I substitute it in with the other equations?

Answer 40

Now that we have y, we use one of the two equation that have only y and z to find z.
Let's use the first one:
7y - 10z = -69, using y = -7:
7(-7) - 10z = -69
Solve for z

Answer 41

-49-10z=-69

Answer 42

Than you add -49 into -69 but the -49 becomes a positive

Answer 43

7(-7) - 10z = -69
-49 - 10z = -69
-10z = -20
z = 2

Answer 44

Thanks!

Answer 45

Correct.

Answer 46

And you get x by doing what...

Answer 47

Now that we have y and z, we go back to one of the original 3 equations that has x, y, and z. We plug in the known values of y and z, and we solve for x.

Answer 48

Let's use the first original equation:
3x - 2y + 2z = 30

Answer 49

3x - 2(-7) + 2(2) = 30
Now you have one equation with only one variable, so you can solve for x.

Answer 50

3x+18=30 x=4

Answer 51

x=4

Answer 52

3x + 14 + 4 = 30
3x + 18 = 30
3x = 12
x = 4

Answer 53

Because 3x=12 divide by 3

Answer 54

Correct.

Answer 55

:D
So y=7, z=, 2, and x=4

Answer 56

Thank you soooo much!!!

Answer 57

The solution is:
x = 4; y = -7; z = 2

Answer 58

You are very welcome.