To represent the purchase of gift cards with the amounts of $2 and $5, let's define:
- \( x \) as the number of $2 gift cards purchased.
- \( y \) as the number of $5 gift cards purchased.
The total amount spent can be expressed as the sum of the costs of the gift cards, which must equal $100. Thus, the equation representing this purchase scenario is:
\[ 2x + 5y = 100 \]
This equation indicates that the total amount spent on the $2 and $5 gift cards must equal $100.