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Let x, y, and z be real numbers such that

x + y - z = 8

x + y + z = 18

-x + 2y + z = 10.

 

Compute xyz.

 Jul 8, 2022
 #1
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From the first equation, we get:

-z + x = 8 - y

And the third equation gievs us:

z - x = 10 - 2y.

 

Since we know that -z + x is -1 times z - x, we know that:

8 - y = 2y - 10

This gives us: y = 6

 

Substiting this value into the first two equations gives us:

x = 7, z = 5

 

From here, we get 210 as our answer. 

 Jul 8, 2022

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