Question:

If (x3+1,y23)=(53,13)(\frac {x}{3}+1, \frac {y-2}{3}) = (\frac {5}{3}, \frac {1}{3}), Find the value of x and y.

Updated On: Oct 18, 2023
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Solution and Explanation

It is given that (x3+1,y23)=(53,13)(\frac {x}{3}+1, \frac {y-2}{3}) = (\frac {5}{3}, \frac {1}{3}).

Since the ordered pairs are equal, the corresponding elements will also be equal.


(x3+1,y23)=(53,13)(\frac {x}{3}+1, \frac {y-2}{3}) = (\frac {5}{3}, \frac {1}{3})


Therefore, 


x3+1=53\frac {x}{3}+1=\frac {5}{3}


⇒ x3=531,y23=13\frac{x}{3} = \frac{5}{3} -1,\frac{y-2}{3} = \frac{1}{3}


x3=23,y=13+23\frac{x}{3} = \frac{2}{3}, y = \frac{1}{3}+\frac{2}{3}


⇒ x=2, y=1

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