ABC26GN0972 · Simplification

$$\begin{aligned} & \frac{3 x}{2 y}=\frac{21}{22} \Rightarrow \frac{x}{y}=\left(\frac{21}{22} \times \frac{2}{3}\right)=\frac{7}{11} \Rightarrow x=\frac{7}{11} y . \\ & 4 x+5 y=83 \Rightarrow 4 \times \frac{7}{11} y+5 y=83 \Rightarrow \frac{28}{11} y+5 y=83 \\ & \Rightarrow 83 y=83 \times 11 \Rightarrow y=11 . \\ & \therefore \quad x=\frac{7}{11} y=\left(\frac{7}{11} \times 11\right)=7 . \end{aligned}$$ So, $\quad y-x=11-7=4$.