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If w, x, y, and z are real numbers satisfying

w + x + y = -2

w + x + z = 4

w + y + z = 29 and

x + y + z = 22

what is xz + yz?

 Jun 14, 2021
 #1
avatar+2135 
0

I don't think those equations are possible.

 

=^._.^=

 Jun 14, 2021
 #3
avatar+2135 
+2

Edit:

My bad, I read all equations as x + y + z. :((

CPhill did a great job answering. :))

 

=^._.^=

catmg  Jun 14, 2021
 #4
avatar+121006 
+1

THX, catmg   !!!

 

 

cool cool cool

CPhill  Jun 14, 2021
 #2
avatar+121006 
+2

w + x + y = -2    ⇒  x + y =  -2 - w      (1)

w + x + z = 4     ⇒  x +  z  = 4  - w     (2)

w + y + z = 29   ⇒  y + z  = 29 - w      (3)

x + y + z = 22   ⇒  2x  + 2y + 2z  =  44  (4)

 

Add (1)  , (2) , (3)

 

2x  + 2y  + 2z  =  31  - 3w      (5)

 

Sub (5)  into (4)

 

31  - 3w   =  44

-3w =  44 - 31

-3w  =   13

w  = -13/3

 

And  using (1)

x + y  =   -2 - (-13/3)   =   7/3

 

x + y +  z  =  22

(7/3) + z  =  22

z = 22 - 7/3  =  59/3

 

So

 

xz +  yz  =

 

(x + y)z  =

 

(7/3) (59/3)   =  

 

413 /  9

 

 

cool cool cool

 Jun 14, 2021

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