# pleae help finding z,x,y

• July 28th 2009, 01:53 AM
alternative
pleae help finding z,x,y
Find x,y and z if 1/x+1/y=1995,1/y+1/z=1996 dhe 1/x+1/z=1997
• July 28th 2009, 02:01 AM
red_dog
Let $\frac{1}{x}=a, \ \frac{1}{y}=b, \ \frac{1}{z}=c$.

Then $\left\{\begin{array}{ll}a+b=1995\\b+c=1996\\a+c=19 97\end{array}\right.$

Solve the system, find a, b, c and then x, y, z.
• July 28th 2009, 02:06 AM
earboth
Quote:

Originally Posted by alternative
Find x,y and z if 1/x+1/y=1995,1/y+1/z=1996 dhe 1/x+1/z=1997

Use the substitution

$u=\dfrac1x$ and $v=\dfrac1y$ and $w=\dfrac1z$

Then you have to solve the system of simultaneous equations:

$\left|\begin{array}{rccccl}u&+&v&&=&1995 \\ &v&+&w&=&1996 \\u&+&w&& =& 1997\end{array}\right.$

Afterwards re-substitute to calculate x, y, z.