How to use differential equations to write $x(t)$ in terms of $y$ and ${y}_{0}$?

$$\{\begin{array}{rcrcl}{x}^{\prime}& =& {\textstyle}-a\phantom{\rule{thinmathspace}{0ex}}x& +& b\phantom{\rule{thinmathspace}{0ex}}xy\\ {y}^{\prime}& =& c\phantom{\rule{thinmathspace}{0ex}}y& -& d\phantom{\rule{thinmathspace}{0ex}}xy\end{array}$$

$$\{\begin{array}{rcrcl}{x}^{\prime}& =& {\textstyle}-a\phantom{\rule{thinmathspace}{0ex}}x& +& b\phantom{\rule{thinmathspace}{0ex}}xy\\ {y}^{\prime}& =& c\phantom{\rule{thinmathspace}{0ex}}y& -& d\phantom{\rule{thinmathspace}{0ex}}xy\end{array}$$