Code:
\[ x=a+Dp=b+Eq\ \Rightarrow\ b-a=Dp-Eq\stackrel{(IDEA)}=(b-a)[\alpha p+\beta q]=Dp-Eq\ \Rightarrow\ [(b-a)\alpha-D]p=[(a-b)\beta-E]q\ \Rightarrow\left.\begin{array}{c}(b-a)\alpha-D=\Lambda q,\\ (a-b)\beta-E=\Lambda p .\end{array}\right\}\ \Rightarrow\ x=a+p((b-a)\alpha-\Lambda q)=c\ mod\ pq \]