Final answer:
To transform system [a] into system [b], one should replace one equation with a multiple of the other equation (option 1), which is part of the method of elimination used in algebra to simplify systems of equations.
Step-by-step explanation:
In order to transform system [a] into system [b], you must determine the appropriate algebraic operation that would achieve this. When dealing with systems of equations, there are standard methods that we use to simplify or manipulate the systems to find solutions. From the options provided, the correct method to get system [b] from system [a] would be to replace one equation with a multiple of the other equation, which corresponds to option 1.
This approach is part of a set of procedures known as the method of elimination in algebra, where one equation is replaced by the sum or difference of the original equation and a multiple of another equation in the system. Essentially, this can eliminate one variable, making it possible to solve for the other. The other options, such as replacing one equation with a multiple of itself, swapping the left-hand sides, or simply swapping the order of equations, would not fundamentally change the system or bring us closer to a solution.
Multiplication or division by the same number on both sides of an equation is a valid operation that will not change the equality of the equation. This process should apply to every term to maintain the balance. For instance:
2A = B
Multiplying both sides by a non-zero constant 'c' gives:
2A × c = B × c
This is a frequent step in solving simultaneous equations, particularly when using the elimination method.