Question 1 of 35beginner🔧 ApplyShort Answer2 marks

If (x3+1,y−23)=(53,13)\left(\frac{x}{3} + 1, y - \frac{2}{3}\right) = \left(\frac{5}{3}, \frac{1}{3}\right), find the values of xx and yy.

Correct Answer

x = 2 and y = 1

Exercise: EXERCISE 2.1 | Q: 1 | (Page 4)
For More Understanding

Explanation

This question tests the fundamental property of ordered pairs - two ordered pairs are equal if and only if their corresponding components are equal. The textbook context shows similar problems where functions are evaluated at specific points (like Examples 20 and 22), demonstrating the process of equating corresponding values.

Solution Steps

  1. Step 1: Since the ordered pairs are equal, equate their corresponding components: (first component) x/3 + 1 = 5/3 and (second component) y - 2/3 = 1/3

  2. Step 2: For x: x/3 + 1 = 5/3 → x/3 = 5/3 - 1 → x/3 = 5/3 - 3/3 → x/3 = 2/3 → x = 2

  3. Step 3: For y: y - 2/3 = 1/3 → y = 1/3 + 2/3 → y = 3/3 → y = 1

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