Question

If $[\frac{x}{3}+1,y-\frac{2}{3}]=\left[\frac{5}{3}\frac{1}{3}\right]$, then find $x$ and $y$.

Answer 1

$\frac{x}{3}+1=\frac{5}{3}-\left(i\right)y-\frac{2}{3}=\frac{1}{3}-\left(ii\right)$

$\frac{x}{3}+1=\frac{5}{3}\Rightarrow \frac{x+3}{3}=\frac{5}{3}\Rightarrow x+3=5\therefore x=5-3=2\therefore x=2y-\frac{2}{3}=\frac{1}{3}y=\frac{1}{3}+\frac{2}{3}y=\frac{1+2}{3}=\frac{3}{3}=1\therefore y=1$