If the ordered pairs (x/3 + 1, y - 2/3) and (5/3, 1/3) are equal, find the values of x and y.
Model Answer & Options
Source: Extra Practicex = 2, y = 1
x = 1, y = 2
x = 2, y = 3
x = 3, y = 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 = 5/3 gives x/3 = 5/3 - 1 = 2/3, so x = 2. Setting y - 2/3 = 1/3 gives y = 1/3 + 2/3 = 1. Therefore, x=2 and y=1. Other options fail to satisfy both linear equations simultaneously.
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