+0  
 
+2
77
5
avatar+2046 

This one just looks confusing af. Could you maybe work out one and I work out the other?

RainbowPanda  Aug 28, 2018
 #1
avatar+90969 
+2

These are difficult....and often lengthy......the other problem is that there is no "set" way to  proceed.....[P.S.....watch your math carefully....one mistake dooms you  !!! ]

 

I'll do the first one  just to demonstrate...

 

2a  + 3b  - 5c   = -5    (1)

-2a - 2b  - c  = -14      (2)

4a  - 4b   + 4c  = -4       divide this equation by 2   ⇒  2a  - 2b  + 2c = -2   (3)

 

Add  (1)  and (2)                               Add (2)  and (3)

2a + 3b - 5c  = -5                              -2a   - 2b  - c  =  -14

-2a - 2b - c  = -14                               2a   - 2b  + 2c  =  -2

________________                         _________________

      b  - 6c    =  -19    (4)                             -4b  + c  = -16   ⇒   c  =   4b   - 16      (5)

 

Sub  (5)  into ( 4)  and we have

 

b - 6(4b - 16) =  -19

b - 24b + 96  = -19

-23b  + 96  = -19   subtract 96 from both sides

-23b = -115    divide both sides by  -23

b  = 5 

 

Use  (5)   to  find  c

c = 4(5) - 16  =   20  - 16 =  4

 

And using  (3) to  find  "a"  we have

2a  - 2(5)  + 2(4) = -2

2a  - 10  + 8  = -2

2a -2 = -2   add 2 to both sides

2a  = 0 ⇒     a   = 0 

 

RP...this requires a bit of experience to master...I would stick to  solving equations in two  variables and make sure you felt comfortable with that before  you attmpted these.....just  my opinion....

 

As a disclaimer...I can show you something known as "Cramer's  Rule"  where no solving is involved...however...it's also  a little  lengthy...but not difficult...!!!!!

 

 

 

cool cool cool

CPhill  Aug 28, 2018
edited by CPhill  Aug 28, 2018
 #2
avatar+2046 
+1

But I have to do these now. Am I supposed to get c as well? I attempted #10 but I didn't do it well lol so I just erased everything. Dang it I have to go soon but want to get this done today!

RainbowPanda  Aug 28, 2018
 #4
avatar+90969 
+2

c =  4  in the first one

 

See (10)  below...

 

 

cool cool cool

CPhill  Aug 28, 2018
edited by CPhill  Aug 28, 2018
 #3
avatar+90969 
+2

10)

 

2a  - 4b  - 2c  =   -4       divide by 2  ⇒   a  - 2b  - c   =  -2    (1)

-3a   + 3b  +6c   = 30    divide by 3  ⇒  - a  + b + 2c  = 10    (2)

-a  - 3b  + c   = 17                                  -a  - 3b  + c  = 17     (3)

 

 

 

Add   (1)  and (2)                               Add  (1) and (3)

a  - 2b  -  c  =  -2                                -a - 2b  - c   = -2   

-a + b  + 2c   = 10                               a   -3b + c  = 17

________________                          ______________

       -b  + c  = 8 ..so..                                -5b    =  15

        c  =  8 + b   (4)                                      b  = -3    (5)

 

 Sub (5)  into (4)     

 

c = 8 + (-3)   

c  =  5

 

And using  (1)  to find  a

 

a  - 2b  - c   =  -2

a  - 2(-3) - (5)    = -2

a  + 6 - 5  = -2

a + 1   = -2

a   =  -3

 

 

 

cool cool cool

CPhill  Aug 28, 2018
 #5
avatar+2046 
0

Tysm i'm sorry I disappeared on you >.<

RainbowPanda  Aug 29, 2018

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