solving same system of equations five different ways.

[svsoccer]

helo. My assignment is to solve the system of equations five ways:
1st graphing calculator
2nd elimination method
3rd reduced echelon form
4th by inverse matrices
5th cramer's rule
SHOW ALL WORK FOR 2-5

1a+1b-2c+3d+2e=9
3a+3b-1c+1d+1e=5
2a+2b-1c+1d-2e=1
4a+4b+1c+0d-3e=4 (and yes that does say zero d)
8a+5b-2c-1d+2e=3

so i finished the first way...i plugged the matrix into my calculator and used reduced row echelon form to get
a=2, b= -1, c=3, d=4, e=1

i have tried to do the other steps but i have been unsuccesful as i am not allowed to use a calculator for those steps. If any one could help me to figure this out and show that steps that need to be done to get the answer i would really appreciate it. I need the answers by Monday December 13 at 7:00 AM

THANK YOU!

 

[svsoccer]

Re: Need Help! solve system of equations five different ways.

helo. My assignment is to solve the system of equations five ways:
1st graphing calculator
2nd elimination method
3rd reduced echelon form
4th by inverse matrices
5th cramer's rule
SHOW ALL WORK FOR 2-5

1a+1b-2c+3d+2e=9 (r1)
3a+3b-1c+1d+1e=5(r2)
2a+2b-1c+1d-2e=1(r3)
4a+4b+1c+0d-3e=4 (and yes that does say zero d)(r4)
8a+5b-2c-1d+2e=3 (r5)




so i finished the first way...i plugged the matrix into my calculator and used reduced row echelon form to get
a=2, b= -1, c=3, d=4, e=1

for the second part i took r2 and r5 and added them together to eliminate d => 11a+8b-3c+3e=8
then i took (r5 x 3) and added it to r1 to again eliminate d => 25a+16b-8c+8e=18
next i took (r3 x -3) and added it to r1 to once again eliminate d => 30a+21b-9c=20
and then r4 already does not have a d value => 4a+4b+1c-3e=4


after eliminating the e's the 3 equations with 3 variables i was left with were....
15a+12b-2c=12
17a+17b+11c=50
30a+21b-9c=20
i then used those equations to cancel out the a's
and was left with.......
-3b-5c=-4 OR b=(-5/3)c+(4/3)
AND
-51b-199c=-546

i then substituted my value of B into the second equation and got
-114c= -478
c=4.192982456

which is not the correct answer...any clue where i am going wrong?

 

[tkhunny]

Re: Need Help! solve system of equations five different ways.

You have an arithmetic error. Track it down and fix it.

"next i took (r3 x -3) and added it to r1 to once again eliminate d => 30a+21b-9c=20"

Why did you do r1 twice. Defintely something fishy going on there.

 

[svsoccer]

Re: Need Help! solve system of equations five different ways.

i solved the second part but now im stuck on reduced echelon form :|

 

[Deleted member 4993]

Re: Need Help! solve system of equations five different ways.

Please show us how far you have progressed with reduced-echelon method.