Final answer:
Doubling the equation 2x + y = 8 to get 4x + 2y = 16 does not change the solution set of the system, because both equations represent the same line on a graph. Hangar diagrams can visually explain this by showing that modifying weights and distances proportionally will not affect the balance point, thus maintaining the same solution.
Step-by-step explanation:
The student is working with a system of linear equations, which is a fundamental topic in algebra. The original equations presented are 4x + 6y = 24 and 2x + y = 8. By doubling the second equation, we obtain another equation, 4x + 2y = 16, which is a multiple of the original. This operation doesn't change the solution set of the system because it represents the same line on a graph; only the scale is different.
To visualize this, consider hangar diagrams where the weight represents the coefficients of the variables and the distance represents the constant term. When the weights and distances on the hangar balance (representing an equation), doubling the weights and distances will still balance (representing the second doubled equation). This demonstrates why the solutions to both equations are the same, because effectively you are describing the same relationship or balance point.