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The system of equations
\frac{xy}{x + y} = 0, \quad \frac{xz}{x + z} = 0, \quad \frac{yz}{y + z} = 1
has exactly one solution. What is $z$ in this solution?

 Mar 8, 2024
 #1
avatar+128406 
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\(\frac{xy}{x + y} = 0, \quad \frac{xz}{x + z} = 0, \quad \frac{yz}{y + z} = 1 \)

 

x  = 0 

 

yz  = y + z

 

zy - z  =  y

 

z ( y - 1)   = y

 

z =   y / (y - 1)

 

y             z

2             2

 

z =  2

 

cool cool cool

 Mar 8, 2024

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