The equation $5x + 3y = 15$ is a linear equation in two variables, $x$ and $y$. Its solution represents a straight line in the Cartesian coordinate system. To find solutions, you need to either express one variable in terms of the other or provide additional conditions like values for $x$ or $y$.

General Solutions:

We solve for $y$ in terms of $x$: $5x + 3y = 15$ $3y = 15 - 5x$ $y = \frac{15 - 5x}{3}$

This means for any chosen value of $x$, you can compute $y$, and vice versa. For example:

• If $x = 0$: $y = \frac{15 - 5(0)}{3} = 5$.
• If $x = 3$: $y = \frac{15 - 5(3)}{3} = 0$.

Similarly, you could solve for $x$ in terms of $y$: $x = \frac{15 - 3y}{5}$

Would you like a graph, a table of values, or a specific solution based on more constraints?

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Follow-up Questions:

1. Would you like a graph of this equation?
2. Should I generate more solutions with specific $x$ or $y$ values?
3. Do you want to explore this in the context of systems of equations?
4. How do you interpret such equations geometrically or in real-world terms?
5. Would you like me to explain how to solve systems involving two such equations?

Tip: For linear equations, always check if solving for one variable or graphing makes the problem easier to visualize!