Final answer:
Only the systems labeled B (30d+22.5e=82.5, 5d+0.5e=4) and D (6d+4.5e=16.5, 6d+0.6e=4.8) are equivalent to the given system because their equations can be derived using valid algebraic operations from the original equations.
Therefore, the systems B and D are equivalent to the original system.
Step-by-step explanation:
The systems equivalent to the given system of equations 6d+4.5e=16.5 and 5d+0.5e=4 are those that can be derived from it using valid algebraic operations, such as multiplication or division by a scalar. Let's examine each option.
- A: The first equation is identical to the given one, so it's equivalent. However, the second equation (45d+4.5e=4) cannot be derived from any of the original equations, so this system is not equivalent.
- B: The first equation (30d+22.5e=82.5) can be obtained by multiplying the first original equation by 5, and the second original equation is preserved, so this system is equivalent.
- C: The first equation can be obtained from the original system by multiplication, but the second one (30d+3e=24) cannot be directly derived from the original equations through any simple algebraic operation, so this system is not equivalent.
- D: The first equation is identical to the original one, but the second equation (6d+0.6e=4.8) is different. To determine its equivalence, we need to inspect whether it can be obtained by a valid operation on the original system; it turns out the second equation can be derived by multiplying 5d+0.5e=4 by 1.2, so this system is equivalent.
- E and F: Both systems have at least one equation that cannot be derived by scaling the original equations, so they are not equivalent.