Question

solve the following system show your work
3x-2y+2z=30
-x+3y-4z=-33
2x-4y+3z=42
I really don't know how to do this if someone could guide me through i would be so thankful

Answer 1

matrix method is usually simplest for this, if you have a calculator

Answer 2

how would i do it?

Answer 3

if we do substitution, then solve the first equation for a variable, and sub it into the variable of the other 2

Answer 4

can you do substitution?

Answer 5

i'm not very good can i get an example?

Answer 6

ax + by + cz = k

solve for z: subtract off the non z terms, and divide off the c

Answer 7

then for some setup:

mx + ny + pz = j we replace z with its equivalent xy setup

Answer 8

im confused

Answer 9

so add xy then divide out c?

Answer 10

the x and y terms so that z is defined in terms of x and y

Answer 11

ok so for this problem i start with the first equation and do that?

Answer 12

we can yes

Answer 13

or should we Choose the easiest way to eliminate a variable, and then write a system of two equations

Answer 14

if you like elimination method then we can do that as well. there are a few different approaches we can take, they all give the same end results

Answer 15

ok i think i know that one the linear combination method?

Answer 16

use eq1 to eliminate the x parts of the last 2

3x-2y+2z=30
-x+3y-4z=-33 < times by 3
2x-4y+3z=42 < times by -3/2

Answer 17

i not sure what a linear comination method is, unless thats another way of saying matrix solution

Answer 18

i think so

Answer 19

ok so i would times the whole equation my 3in order to get the y eliminated for the second euation

Answer 20

if so the second equation is 15x+15z=216 right?

Answer 21

3x-2y+2z=30
-x+3y-4z=-33 < times by 3
2x-4y+3z=42 < times by -3/2



3x-2y+2z=30
-3x+9y-12z=-99
-3x+6y-9z/2=-63




3x-2y+2z=30
0x+7y-10z=-69
0x+4y-5z/2=-33


7y-10z=-69
8y- 5z=-66

now its a 2 variable setup

Answer 22

oh ok that makes sense

Answer 23

7y-10z=-69
8y- 5z=-66 << times -2


7y-10z=-69
-16y+10z=132
--------------
-9y =63

y = -7

Answer 24

using eq2 we find 7(-7)-10z = -69, solve for z

knowing y and z, solve for x in the first equation

Answer 25

OK thank you i appreciate your help!

Answer 26

youre welcome, when you find a solution, let me know what you get.

Answer 27

ok i will one moment

Answer 28

im stuck so on the first equation the ending equation was 2x-2z=-3 was that right?

Answer 29

we know y = -7, what did you get for z?

Answer 30

i added the first and second equation

Answer 31

i add the 1st and 2nd, the 1st and 3rd and got rid of x

3x-2y+2z=30
-x+3y-4z=-33 < times by 3
2x-4y+3z=42 < times by -3/2



3x-2y+2z=30
-3x+9y-12z=-99
-3x+6y-9z/2=-63




3x-2y+2z=30
0x+7y-10z=-69
0x+4y-5z/2=-33


7y-10z=-69
8y- 5z=-66

now its a 2 variable setup

Answer 32

since we have a 10 and 5, i figure times 2 will get rid of z for us

Answer 33

7y-10z=-69
8y- 5z=-66 << times -2


7y-10z=-69
-16y+10z=132
--------------
-9y =63

y = -7

Answer 34

can you get this far?

Answer 35

yes

Answer 36

then using:

7y-10z = -69 we can find z

what is z?

Answer 37

z= 2?

Answer 38

good, y = -7, z=2

now we can use any of the original equations .... if we use equation 1

3x-2y+2z=30

3x-2(-7)+2(2)=30

solve for x

Answer 39

x=4?

Answer 40

yes, good job

Answer 41

thank you!

Answer 42

yw