Source: Extra Practice

If the ordered pairs (x/3+1,y2/3)(x/3 + 1, y - 2/3) and (5/3,1/3)(5/3, 1/3) are equal, find the values of xx and yy.

Options

Option A is correct

x=2x = 2, y=1y = 1

Option B

x=1x = 1, y=2y = 2

Option C

x=2x = 2, y=3y = 3

Option D

x=3x = 3, y=1y = 1

Explanation

Two ordered pairs are equal if and only if their corresponding first elements are equal and their corresponding second elements are equal. Setting x/3+1=5/3x/3 + 1 = 5/3 gives x/3=5/31=2/3x/3 = 5/3 - 1 = 2/3, so x=2x = 2. Setting y2/3=1/3y - 2/3 = 1/3 gives y=1/3+2/3=1y = 1/3 + 2/3 = 1. Therefore, x=2x=2 and y=1y=1. Other options fail to satisfy both linear equations simultaneously.