Question

how do i solve the system of equations?
2x + 4y + 3z = 6
3x + 5y + 6z =3
2x + 3y + 4z = 8

Answer 1

are you familiar with matrices

Answer 2

kinda

Answer 3

well you can use the gaussian elimination

Answer 4

ok

Answer 5

meaning you use the elementary row operations

Answer 6

yea

Answer 7

2 4 3 | 6
3 5 6 | 3
2 3 4 | 8
subtract row 1 from row 3 and tell me what u get

Answer 8

ok one sec

Answer 9

0 -1 1 |2
is that right?

Answer 10

yeah.now divide row 1 by 2

Answer 11

ok the answer i have above isnt row one is it or is row one in the problem still?

Answer 12

no.it is still row 3.row one is ur original problem
2 4 3 | 6

Answer 13

ok

Answer 14

2/3 4/5 1/2 |2 right?

Answer 15

it is actually
1 2 3/2 | 3
get it?

Answer 16

how?

Answer 17

well u take the first row.and u divide by 2.then it changes from
2 4 3 |6

to

1 2 3/2 | 3

Answer 18

ohh! u divid by two not thr 2nd row :/lol now i got that ok

Answer 19

then your rows are now like this

1 2 3/2 | 3
3 5 6 | 3
0 -1 1 | 2

Answer 20

yea

Answer 21

sorry.
multipy row 1 by 3 the subtract it from row 2
the u have a reduced row 2

Answer 22

ok? one sec

Answer 23

when i subtract which number should be on top?

Answer 24

1 2 3/2 | 3
_ _ _ | _
0 -1 1 | 2
the only r0w that changes is row 2

Answer 25

yea,ok i get that so row to is now 3 8 9/2 |-3

Answer 26

3-(3X3) = 0
That is how u do it.

Answer 27

what?

Answer 28

meaning u take 1 from row1 and multiply by 3 the u subtract the answer from 3 in row 2 and u get ur as 0.
do the same with the second term

Answer 29

then u get

1 2 3/2 | 3
0 -1 3/2 | -6
0 -1 1 | 2

Answer 30

ohh

Answer 31

ok then from there what do i do next ?

Answer 32

multiply row 2 by -1

Answer 33

ok

Answer 34

0 1 -3/2 |6

Answer 35

exactly

Answer 36

ok is this the answer or is the more?

Answer 37

1 2 3/2 | 3
0 1 -3/2 | 6
0 -1 1 |2

in row 1 u must eliminate 2
and in row 3 must eliminate -1.

Answer 38

why?

Answer 39

add row 3 and row 2 to get
1 2 3/2 |3
0 1 -3/2 |6
0 0 1/2 |-4

and u jst eliminated 1 from row 3

Answer 40

ok

Answer 41

sorry u jst eliminated -1 from row 3

Answer 42

then now we eliminate 2 from row 1

Answer 43

i figured u ment that

Answer 44

:)

Answer 45

do this row1-2(row2)

Answer 46

then u get
1 0 9/2 |-9
0 1 -3/2 | 6
0 0 1/2 |-4

Answer 47

getting this?

Answer 48

yea

Answer 49

basically u want to get to a point were u have
1 0 0 | ?
0 1 0 | ?
0 0 1 | ?

Answer 50

now divide row 3 by 1/2 (half)

Answer 51

ohh ok

Answer 52

1 |-2

Answer 53

what is 4 divided by half

Answer 54

oh 8

Answer 55

then u have
1 0 9/2 | -9
0 1 -3/2 | 6
0 0 1 | -8

what do u think u should do to eliminate 9/2?

Answer 56

2/9?

Answer 57

what about 2/9?

Answer 58

u mulitply?

Answer 59

remember you want it to be 0

Answer 60

on then subtract 9/2?

Answer 61

exactly

Answer 62

ok :)

Answer 63

what bout the numbers on the end?

Answer 64

so mentally multiply row 3 by 9/2

Answer 65

and then subtract it from row 1

Answer 66

what do u get for row1?

Answer 67

1 0 0 |1?

Answer 68

actually
1 0 0 |27

Answer 69

oh

Answer 70

now u got

1 0 0 | 27
0 1 -3/2 |6
0 0 1 |-8

Answer 71

u must now eliminate -3/2.how do u think u do that?

Answer 72

yes

Answer 73

how do you think u can do it?

Answer 74

plus 3/2

Answer 75

sure.which row can u use to eliminate it?

Answer 76

3

Answer 77

good.how do u do that?

Answer 78

idk

Answer 79

multiply row3 by 3/2 and add it to row2

Answer 80

ok

Answer 81

that way 1 becomes 3/2
and you can add that to row 2.the -3/2 + 3/2 = 0 which eliminates 3/2

Answer 82

yea

Answer 83

then u have
1 0 0 |27
0 1 0 |-6
0 0 1 |-8

what is ur x,y and z?

Answer 84

27,-6,-8?

Answer 85

yes

Answer 86

ok

Answer 87

but i think i made a mistake with the numbers somewhere

Answer 88

should i paste the whole solution or can u figure out the mistake?

Answer 89

i can figure it out now

Answer 90

ok.sure