# solving systems of linear equations

• Apr 24th 2007, 05:25 PM
ohchelsea
solving systems of linear equations
watch this be really easy and im just making it hard....
but anyway, i've tried this one, i swear, like five times (no lie) and i got different answers everytime. help!!

the problem says:
"solve the system of linear equations using a combination of the Methods of Eliminations and Back Substitution."

x-2y+z=8
2x-6y-11z=4
3x-6y+10=6
• Apr 24th 2007, 05:34 PM
Jhevon
Quote:

Originally Posted by ohchelsea
watch this be really easy and im just making it hard....
but anyway, i've tried this one, i swear, like five times (no lie) and i got different answers everytime. help!!

the problem says:
"solve the system of linear equations using a combination of the Methods of Eliminations and Back Substitution."

x-2y+z=8
2x-6y-11z=4
3x-6y+10=6

should the last equation be 3x - 6y + 10z = 6 ?
• Apr 24th 2007, 05:42 PM
ohchelsea
yes. typo. sorry :)
• Apr 24th 2007, 05:52 PM
Jhevon
Quote:

Originally Posted by ohchelsea
watch this be really easy and im just making it hard....
but anyway, i've tried this one, i swear, like five times (no lie) and i got different answers everytime. help!!

the problem says:
"solve the system of linear equations using a combination of the Methods of Eliminations and Back Substitution."

x-2y+z=8
2x-6y-11z=4
3x-6y+10=6

x - 2y + z = 8 .................(1)
2x - 6y - 11z = 4 .............(2)
3x - 6y + 10z = 6 .............(3)

3x - 6y + 3z = 24 .............(4) = (1)*3
2x - 6y - 11z = 4 .............(2)
3x - 6y + 10z = 6 .............(3)

=> 7z = -18...............(3) - (4), what luck! i'm only left with z
=> z = -18/7

=> x + 21z = 2 ...........(3) - (2)
=> x + 21(-18/7) = 2
=> x - 54 = 2
=> x = 56

but x - 2y + z = 8
=> 56 - 2y - 18/7 = 8
=> 2y = 56 - 18/7 - 8 = 318/7
=> y = 159/7

so x = 56, y = 159/7, z = -18/7
• Apr 24th 2007, 06:00 PM
ohchelsea
thank you soooo much!
• Apr 24th 2007, 06:09 PM
Jhevon
Quote:

Originally Posted by ohchelsea
thank you soooo much!

you are very welcome. did you get my process. what you want to do with these equations is eliminate one variable completely and in doing so get two simultaneous equations with two unknowns.

i choose to eliminate y first since two equations already had -6y. so i changed the first one to get -6y. now, subtracting any two of the equations i would eliminate y, and be left with x and z only. by luck, the first time, i eliminated both x and y and was only left with z, that made the problem easier