How to make sense of the 'Relaxation Method' for measuring reaction kinetics?
You have two simultaneous reactions, 

$$\begin{array}{rcl}
\ce{A} &amp;\xrightarrow{k_1}&amp; \ce{B}\\[6pt]
\ce{B} &amp;\xrightarrow{k_{-1}}&amp; \ce{A}
\end{array}$$

and $\dfrac{\mathrm d[\ce{A}]}{\mathrm dt}$ equals $-k_1 [\ce{A}]$ for the first reaction alone and $k_{-1} [\ce{B}]$ for the second alone. To get the total $\dfrac{\mathrm d[\ce{A}]}{\mathrm dt}$ for the reactions running simultaneously, you have to add the contributions from each reaction:

$$\dfrac{\mathrm d[\ce{A}]}{\mathrm dt} = -k_1 [\ce{A}] + k_{-1} [\ce{B}]$$

This will always be true; at equilibrium you'll have $\dfrac{\mathrm d[\ce{A}]}{\mathrm dt} = 0$ and

$$K = \frac{k_1}{k_{-1}} = \frac{[\ce{B}]}{[\ce{A}]}$$

If you did it your way, this wouldn't be the case.