• The expression 3x - y is equivalent to 3x - 1y because subtracting \(y\) is the same as subtracting 1 times \(y\).
• Therefore, 3x - y is equivalent to 3x - 1y.

Supplemental Knowledge

In algebra, simplifying expressions involves combining like terms and ensuring that the expression is in its simplest form. The expression given is \(3x - y\). To determine which choice is equivalent to this expression, we need to compare it with the provided options.
Let's break down the options:

1. 4x: This expression represents four times the variable \(x\). It does not include a term involving \(y\), so it cannot be equivalent to \(3x - y\).
2. 3x - 1y: This expression represents three times the variable \(x\) minus one times the variable \(y\). In algebra, coefficients of 1 are often implied and do not need to be explicitly written. Therefore, \(3x - 1y\) is equivalent to \(3x - y\).

Real-Life Connections

Consider you are baking cookies and you have a recipe that calls for 3 cups of flour minus 1 cup of sugar (represented as \(3F - S\)). If someone asks if using 4 cups of flour alone (4F) or using 3 cups of flour minus 1 cup of sugar (3F - S) will give you the same result, it's clear that only the latter matches your original recipe. This analogy helps illustrate how expressions must match in structure and components to be considered equivalent.

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