Question 1 of 33beginner🔧 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 concept that two ordered pairs are equal if and only if their corresponding components are equal. The textbook context covers functions and relations extensively, including the concept of ordered pairs in function definitions like f = {(x, x³): x ∈ R}. When ordered pairs are equal, we equate the first components together and the second components together to solve for the unknowns.

Solution Steps

  1. Step 1: Since the two ordered pairs are equal, equate their corresponding components: First component: (x/3) + 1 = 5/3; Second component: y - (2/3) = 1/3

  2. Step 2: Solving for x: (x/3) + 1 = 5/3 → (x/3) = 5/3 - 1 = 5/3 - 3/3 = 2/3 → x = 2

  3. Step 3: Solving for y: y - (2/3) = 1/3 → y = 1/3 + 2/3 = 3/3 = 1

  4. Step 4: Therefore, x = 2 and y = 1.

Next