To determine the correct option that explains how System B was formed from System A, we need to analyze the relationships between the two systems of equations.
The key steps to follow involve looking at how one equation might be derived from another by manipulating the first equation (either by multiplying it by a constant, adding it to the second equation, or both).
Here’s a step-by-step process you can follow:
- Examine the first equation in System A and see what happens when you multiply it by the constants given in each option.
- Add that product to the second equation in System A to check if that results in the second equation presented in System B.
- Verify if the new system retains the same solution as the original system.
For each option:
- A) Check if multiplying the first equation by 3 and adding it to the second equation gives you the second equation in System B. If this results in the form and maintains the solution, then this option is correct.
- B) Do the same check with a multiplication factor of 5.
- C) Check what happens if you multiply the first equation by -5 and add it to the second equation.
- D) Finally, verify if multiplying by -6 yields the required change.
Once you gather these results, you can conclude which option accurately describes the transition from System A to System B and whether the solutions remain consistent.
If you don't have access to the specific equations from System A and System B, you cannot definitively choose an option based solely on this information; you will need to go through the algebra as mentioned.