Consider the two equations below:

${y}_{1}=(1-\frac{{a}_{1}}{x}){e}^{-{\displaystyle \frac{\alpha \phantom{\rule{thinmathspace}{0ex}}{a}_{1}}{x}}}\phantom{\rule{0ex}{0ex}}{y}_{2}=(1-\frac{{a}_{2}}{x}){e}^{-{\displaystyle \frac{\alpha \phantom{\rule{thinmathspace}{0ex}}{a}_{2}}{x}}}$

Given ${y}_{1}$, ${y}_{2}$, ${a}_{1}$ and ${a}_{2}$, is there an analytical way to determine $\alpha $ and $x$?

${y}_{1}=(1-\frac{{a}_{1}}{x}){e}^{-{\displaystyle \frac{\alpha \phantom{\rule{thinmathspace}{0ex}}{a}_{1}}{x}}}\phantom{\rule{0ex}{0ex}}{y}_{2}=(1-\frac{{a}_{2}}{x}){e}^{-{\displaystyle \frac{\alpha \phantom{\rule{thinmathspace}{0ex}}{a}_{2}}{x}}}$

Given ${y}_{1}$, ${y}_{2}$, ${a}_{1}$ and ${a}_{2}$, is there an analytical way to determine $\alpha $ and $x$?