Let's break this down step by step for both (a) and (b).

(a) How do we transform System A into System B?

From the systems given:

• System A: $\text{Equation [A1]}: 2x + 4y = -10$ $\text{Equation [A2]}: -6x - 5y = 9$

• System B: $\text{Equation [B1]}: 2x + 4y = -10$ $\text{Equation [B2]}: 7y = -21$

To transform System A into System B, notice that:

• Equation [A1] is identical to Equation [B1].
• We need to change Equation [A2] into Equation [B2]. If we solve Equation [A2] for $y$, we get: $-6x - 5y = 9 \quad \Rightarrow \quad y = -3$ This is equivalent to Equation [B2] because $7y = -21$ simplifies to $y = -3$.

So, to transform System A into System B, Equation [A1] stays the same, and Equation [A2] is transformed into Equation [B2].

Thus, the correct transformation is: [ \boxed{\text{Equation [A1] + Equation [A2] → Equation [B1] + Equation [B2]}} ]

(b) How do we transform System B into System C?

From the systems given:

• System B: $\text{Equation [B1]}: 2x + 4y = -10$ $\text{Equation [B2]}: 7y = -21$

• System C: $\text{Equation [C1]}: 2x + 4y = -10$ $\text{Equation [C2]}: y = -3$

To transform System B into System C, notice:

• Equation [B1] is identical to Equation [C1].
• Equation [B2] can be solved for $y$: $7y = -21 \quad \Rightarrow \quad y = -3$ This is Equation [C2].

So, to transform System B into System C, Equation [B1] stays the same, and Equation [B2] transforms into Equation [C2].

Thus, the correct transformation is: [ \boxed{\text{Equation [B1] + Equation [B2] → Equation [C1] + Equation [C2]}} ]

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Summary of Answers:

• (a) System A to System B: Equation [A1] + Equation [A2] → Equation [B1] + Equation [B2]
• (b) System B to System C: Equation [B1] + Equation [B2] → Equation [C1] + Equation [C2]

Would you like to go over any details or ask any further questions on this?

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Here are some related questions you might find useful:

1. How can we use substitution to solve a system of equations?
2. What’s the difference between a system of linear equations and a system of nonlinear equations?
3. How do you solve a system of equations using the elimination method?
4. What is the graphical interpretation of solving a system of linear equations?
5. Can we transform a system of equations by multiplying the equations by constants?

Tip: When solving systems of equations, always check if one of the equations is already in a simplified form (like $y = -3$), which can save you time in solving the system.