Question: A subway's total capacity is modeled by $6x+2y=120$, where $x$ is the seating capacity and $y$ is the standing capacity. Which equation represents the same relationship?
1. **State the problem:** We are given the equation $$6x + 2y = 120$$ representing the total capacity of a subway, where $$x$$ is seating capacity and $$y$$ is standing capacity.
2. **Goal:** Find an equivalent equation that represents the same relationship.
3. **Formula and rules:** To find an equivalent equation, we can divide both sides of the equation by the same nonzero number. This does not change the equality.
4. **Divide both sides by 2:**
$$\frac{6x}{2} + \frac{2y}{2} = \frac{120}{2}$$
5. **Simplify each term:**
$$3x + y = 60$$
6. **Use \cancel to show cancellation:**
$$\cancel{\frac{6x}{2}} + \cancel{\frac{2y}{2}} = \cancel{\frac{120}{2}}$$
7. **Rewrite to solve for $$y$$:**
$$y = 60 - 3x$$
8. **Final equivalent equation:**
$$y = 60 - 3x$$
This equation represents the same relationship as the original.