anonymous
  • anonymous
how do i solve the system of equations? 2x + 4y + 3z = 6 3x + 5y + 6z =3 2x + 3y + 4z = 8
Precalculus
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
are you familiar with matrices
anonymous
  • anonymous
kinda
anonymous
  • anonymous
well you can use the gaussian elimination

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anonymous
  • anonymous
ok
anonymous
  • anonymous
meaning you use the elementary row operations
anonymous
  • anonymous
yea
anonymous
  • 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
  • anonymous
ok one sec
anonymous
  • anonymous
0 -1 1 |2 is that right?
anonymous
  • anonymous
yeah.now divide row 1 by 2
anonymous
  • anonymous
ok the answer i have above isnt row one is it or is row one in the problem still?
anonymous
  • anonymous
no.it is still row 3.row one is ur original problem 2 4 3 | 6
anonymous
  • anonymous
ok
anonymous
  • anonymous
2/3 4/5 1/2 |2 right?
anonymous
  • anonymous
it is actually 1 2 3/2 | 3 get it?
anonymous
  • anonymous
how?
anonymous
  • 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
  • anonymous
ohh! u divid by two not thr 2nd row :/lol now i got that ok
anonymous
  • anonymous
then your rows are now like this 1 2 3/2 | 3 3 5 6 | 3 0 -1 1 | 2
anonymous
  • anonymous
yea
anonymous
  • anonymous
sorry. multipy row 1 by 3 the subtract it from row 2 the u have a reduced row 2
anonymous
  • anonymous
ok? one sec
anonymous
  • anonymous
when i subtract which number should be on top?
anonymous
  • anonymous
1 2 3/2 | 3 _ _ _ | _ 0 -1 1 | 2 the only r0w that changes is row 2
anonymous
  • anonymous
yea,ok i get that so row to is now 3 8 9/2 |-3
anonymous
  • anonymous
3-(3X3) = 0 That is how u do it.
anonymous
  • anonymous
what?
anonymous
  • 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
  • anonymous
then u get 1 2 3/2 | 3 0 -1 3/2 | -6 0 -1 1 | 2
anonymous
  • anonymous
ohh
anonymous
  • anonymous
ok then from there what do i do next ?
anonymous
  • anonymous
multiply row 2 by -1
anonymous
  • anonymous
ok
anonymous
  • anonymous
0 1 -3/2 |6
anonymous
  • anonymous
exactly
anonymous
  • anonymous
ok is this the answer or is the more?
anonymous
  • 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
  • anonymous
why?
anonymous
  • 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
  • anonymous
ok
anonymous
  • anonymous
sorry u jst eliminated -1 from row 3
anonymous
  • anonymous
then now we eliminate 2 from row 1
anonymous
  • anonymous
i figured u ment that
anonymous
  • anonymous
:)
anonymous
  • anonymous
do this row1-2(row2)
anonymous
  • anonymous
then u get 1 0 9/2 |-9 0 1 -3/2 | 6 0 0 1/2 |-4
anonymous
  • anonymous
getting this?
anonymous
  • anonymous
yea
anonymous
  • anonymous
basically u want to get to a point were u have 1 0 0 | ? 0 1 0 | ? 0 0 1 | ?
anonymous
  • anonymous
now divide row 3 by 1/2 (half)
anonymous
  • anonymous
ohh ok
anonymous
  • anonymous
1 |-2
anonymous
  • anonymous
what is 4 divided by half
anonymous
  • anonymous
oh 8
anonymous
  • 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
  • anonymous
2/9?
anonymous
  • anonymous
what about 2/9?
anonymous
  • anonymous
u mulitply?
anonymous
  • anonymous
remember you want it to be 0
anonymous
  • anonymous
on then subtract 9/2?
anonymous
  • anonymous
exactly
anonymous
  • anonymous
ok :)
anonymous
  • anonymous
what bout the numbers on the end?
anonymous
  • anonymous
so mentally multiply row 3 by 9/2
anonymous
  • anonymous
and then subtract it from row 1
anonymous
  • anonymous
what do u get for row1?
anonymous
  • anonymous
1 0 0 |1?
anonymous
  • anonymous
actually 1 0 0 |27
anonymous
  • anonymous
oh
anonymous
  • anonymous
now u got 1 0 0 | 27 0 1 -3/2 |6 0 0 1 |-8
anonymous
  • anonymous
u must now eliminate -3/2.how do u think u do that?
anonymous
  • anonymous
yes
anonymous
  • anonymous
how do you think u can do it?
anonymous
  • anonymous
plus 3/2
anonymous
  • anonymous
sure.which row can u use to eliminate it?
anonymous
  • anonymous
3
anonymous
  • anonymous
good.how do u do that?
anonymous
  • anonymous
idk
anonymous
  • anonymous
multiply row3 by 3/2 and add it to row2
anonymous
  • anonymous
ok
anonymous
  • 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
  • anonymous
yea
anonymous
  • anonymous
then u have 1 0 0 |27 0 1 0 |-6 0 0 1 |-8 what is ur x,y and z?
anonymous
  • anonymous
27,-6,-8?
anonymous
  • anonymous
yes
anonymous
  • anonymous
ok
anonymous
  • anonymous
but i think i made a mistake with the numbers somewhere
anonymous
  • anonymous
should i paste the whole solution or can u figure out the mistake?
anonymous
  • anonymous
i can figure it out now
anonymous
  • anonymous
ok.sure

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