Question

If $(\frac{x}{3}+1,y-\frac{2}{3})=(\frac{5}{3},\frac{1}{3})$, find the values of $x$ and $y$.

Answer 1

Given:
$(\frac{x}{3}+1,y-\frac{2}{3})=(\frac{5}{3},\frac{1}{3})$
As the ordered pairs are equal, corresponding elements should also be equal.
Thus,
$\frac{x}{3}+1=\frac{5}{3}$ and $y-\frac{2}{3}=\frac{1}{3}$
$\Rightarrow \frac{x}{3}=\frac{5}{3}-1$ and $y=\frac{1}{3}+\frac{2}{3}$
$\Rightarrow \frac{x}{3}=\frac{5-3}{3}$ and $y=\frac{1+2}{3}$
$\Rightarrow \frac{x}{3}=\frac{2}{3}$ and $y=\frac{3}{3}$
$\Rightarrow x=2$ and $y=1$.