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

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- anonymous

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

- jamiebookeater

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- anonymous

are you familiar with matrices

- anonymous

kinda

- anonymous

well you can use the gaussian elimination

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## More answers

- anonymous

ok

- anonymous

meaning you use the elementary row operations

- anonymous

yea

- anonymous

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

- anonymous

ok one sec

- anonymous

0 -1 1 |2
is that right?

- anonymous

yeah.now divide row 1 by 2

- anonymous

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

- anonymous

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

- anonymous

ok

- anonymous

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

- anonymous

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

- anonymous

how?

- anonymous

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

- anonymous

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

- anonymous

then your rows are now like this
1 2 3/2 | 3
3 5 6 | 3
0 -1 1 | 2

- anonymous

yea

- anonymous

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

- anonymous

ok? one sec

- anonymous

when i subtract which number should be on top?

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

what?

- anonymous

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

- anonymous

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

- anonymous

ohh

- anonymous

ok then from there what do i do next ?

- anonymous

multiply row 2 by -1

- anonymous

ok

- anonymous

0 1 -3/2 |6

- anonymous

exactly

- anonymous

ok is this the answer or is the more?

- anonymous

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.

- anonymous

why?

- anonymous

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

- anonymous

ok

- anonymous

sorry u jst eliminated -1 from row 3

- anonymous

then now we eliminate 2 from row 1

- anonymous

i figured u ment that

- anonymous

:)

- anonymous

do this row1-2(row2)

- anonymous

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

- anonymous

getting this?

- anonymous

yea

- anonymous

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

- anonymous

now divide row 3 by 1/2 (half)

- anonymous

ohh ok

- anonymous

1 |-2

- anonymous

what is 4 divided by half

- anonymous

oh 8

- anonymous

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?

- anonymous

2/9?

- anonymous

what about 2/9?

- anonymous

u mulitply?

- anonymous

remember you want it to be 0

- anonymous

on then subtract 9/2?

- anonymous

exactly

- anonymous

ok :)

- anonymous

what bout the numbers on the end?

- anonymous

so mentally multiply row 3 by 9/2

- anonymous

and then subtract it from row 1

- anonymous

what do u get for row1?

- anonymous

1 0 0 |1?

- anonymous

actually
1 0 0 |27

- anonymous

oh

- anonymous

now u got
1 0 0 | 27
0 1 -3/2 |6
0 0 1 |-8

- anonymous

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

- anonymous

yes

- anonymous

how do you think u can do it?

- anonymous

plus 3/2

- anonymous

sure.which row can u use to eliminate it?

- anonymous

3

- anonymous

good.how do u do that?

- anonymous

idk

- anonymous

multiply row3 by 3/2 and add it to row2

- anonymous

ok

- anonymous

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

- anonymous

yea

- anonymous

then u have
1 0 0 |27
0 1 0 |-6
0 0 1 |-8
what is ur x,y and z?

- anonymous

27,-6,-8?

- anonymous

yes

- anonymous

ok

- anonymous

but i think i made a mistake with the numbers somewhere

- anonymous

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

- anonymous

i can figure it out now

- anonymous

ok.sure

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