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

Since the given two ordered pairs are equal, we have

$\frac{x}{3}+1=\frac{5}{3}\Rightarrow \frac{x}{3}=(\frac{5}{3}-1)=\frac{2}{3}\Rightarrow \frac{x}{3}=\frac{2}{3}\Rightarrow x=2$

and $y-\frac{2}{3}=\frac{1}{3}\Rightarrow y=(\frac{1}{3}+\frac{2}{3})=\frac{3}{3}=1\Rightarrow y=1$

Hence, $x=2$ and $y=1$