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\[\begin{align}
x+x+y&=14\\
L+L+z&=20\\
 x+y+z&=12\\
 x+z+L&=18
\end{align}\]

If numbers $x,y,z,L$ satisfy the equations above, find the value of $x+z$.

 Jan 21, 2021
 #1
avatar+267 
+2

after bashing randomly, I got x=6, y=2, z=4, and L=8. 

 

since x=6 and z=4, 6+4=10

 Jan 21, 2021
edited by KitSoundwave  Jan 21, 2021
edited by KitSoundwave  Jan 21, 2021
 #2
avatar+116126 
+2

2x +  y  = 14      ⇒ y = 14 - 2x

2L  + z =  20   ⇒ z = 20 - 2L

x + y + z  = 12

x + z + L  =  18

 

Using the last two equations and substituting

 

x + 14 - 2x + 20 - 2L =  12

-x - 2L   =  -22        (1)

 

x + (20- 2L) + L  =18

x - L  =  -2          (2)

 

Add (1)  and (2)

 

-3L  = -24

L = 8

 

x - 8  =  -2

x =  6

 

z = 20  - 2L  =   4

 

y = 14 - 2x   =  2

 

x +  z =   10

 

 

cool cool cool

 Jan 21, 2021

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