Question

how do I solve a three equation problem using elimanation.
-5x+8y+3z=122
7x-2y-12z=-783
-8x-9y-10z=15 ?
I just want to know how to solve step by step -_-

Answer 1

Essentially the same way you solve a 2x2 linear system. It is a fairly time consuming and detail oriented proccess.

Answer 2

A -5x+8y+3z=122
B 7x-2y-12z=-783
C -8x-9y-10z=15

pick 2 to solve for, then it spits out another (D)
A
B
---
D

Solve the other two, then it spits out another (E)
B
C
---
E

then solve for D and E.
After that, x, y, z should all check in the original 3 equations.

Answer 3

I hope that helps!

Answer 4

and what am i suppose to solve after i get d e ?
i get all big numbers

Answer 5

for the top two i got 23x-45z=-3,010
and fot the bottom two i got 79x-88z=-7077
now im suppose to get rid of one letter but heres where im stuck at

Answer 6

Your numbers are going to be different depending out what you used to eliminate. But it is good that you eliminated just one variable (y) between the two. I forgot to mention that. Now you take the two you got and eliminate another variable. (x or z). If you want to eliminate x, multiply -79 on the top and 23 on the bottom. Then then the x's will cancel out.

Answer 7

okay so for the top i got 1817x-3555z=-237790 and
the bottom is 1817x-2024=-162771
then i work it out and i get -5579z=-400561 if i divide z to both sides i get a decimal am i suppose to get that or a whole number ?

Answer 8

Our numbers will be different, guaranteed. There are an infinite amount of ways to solve it. I tried running through it... but I'm not great with details. So, my answer didn't add up. But this is basically how you are supposed to do it:

A -5x+8y+3z=122
B 7x-2y-12z=-783
C -8x-9y-10z=15

pick 2 to solve for, then it spits out another (D)

7* A -5x+8y+3z=122 -35x+56y+21z=854
5* B 7x-2y-12z=-783 35x-10y-60z=-3915
---
D 46y-39z=-3061

Solve the other two, then it spits out another (E)
8* B 7x-2y-12z=-783 56x-16y-96z=-6264
7* C -8x-9y-10z=15 -56x-63y-70z=105
---
E -79y-166z=-6159

then solve for D and E.

79* D 46y-39z=-3061 3634y-3081z=-241819
46* E -79y-166z=-6159 -3634y-7636z=-283314
---
-10717z=-525133
/-10717 /-10717
z=49

Repeat, but solve for y:

-166* D 46y-39z=-3061 -7636y+6474z=508126
39* E -79y-166z=-6159 -3081y-6474z=-240201
---
-10717y=267925
/-10717 /-10717
y=-25

(z=49, y=-25)

C -8x-9(-25)-10(49)=15
-8x+225-490=150
-8x-265=150
+265 +265
-8x=-115
/-8 /-8
x=14.375

(z=49, y=-25, x=14.375)

After that, x, y, z should all check in the original 3 equations... which mine didn't... Sorry :(

Answer 9

OK OK OK, I got. I don't know where I messed up early, but this is the solution. Very detailed oriented, as mentioned. Hope this helps you out!

A -5x+8y+3z=122
B 7x-2y-12z=-783
C -8x-9y-10z=15

pick 2 to solve for, then it spits out another (D)

7* A -5x+8y+3z=122 -35x+56y+21z=854
5* B 7x-2y-12z=-783 35x-10y-60z=-3915
---
D 46y-39z=-3061

Solve the other two, then it spits out another (E)
8* B 7x-2y-12z=-783 56x-16y-96z=-6264
7* C -8x-9y-10z=15 -56x-63y-70z=105
---
E -79y-166z=-6159

then solve for D and E.

79* D 46y-39z=-3061 3634y-3081z=-241819
46* E -79y-166z=-6159 -3634y-7636z=-283314
---
-10717z=-525133
/-10717 /-10717
z=49

Repeat, but solve for y:

-166* D 46y-39z=-3061 -7636y+6474z=508126
39* E -79y-166z=-6159 -3081y-6474z=-240201
---
-10717y=267925
/-10717 /-10717
y=-25

(z=49, y=-25)

A -5x+8(-25)+3(49)=122
-5x-200+147=122
-5x-53=122
+53 +53
-5x=175
/-5 /-5
x=-35


(z=49, y=-25, x=-35)

After that, x, y, z should all check in the original 3 equations.

A -5(-35)+8(-25)+3(49)=122 (Checks)
B 7(-35)-2(-25)-12(49)=-783 (Checks)
C -8(-35)-9(-25)-10(49)=15 (Checks!)

Answer 10

thank you for helping me guys i appericate it and i understand now :)