Final answer:
In solving systems of equations, the best strategy is often to isolate one variable in an equation where it can be easily achieved. Therefore, answers b), d), and a) are appropriate choices for the given equation sets to resolve y or x most straightforwardly.
Step-by-step explanation:
In solving systems of linear equations, such as 5x+y=2 and 3x+y=7, the goal is to isolate one variable to make the solution process simpler. For example, you could choose option b) for the pair 5x+y=2 and 3x+y=7, which suggests solving for y in the second equation because it can be easily isolated. Similarly, for the pair 2x-3y=6 and x+7y=2, option d) to solve for y in the second equation is advantageous because y can be isolated by subtracting x from both sides.
For the pair 4x-y=-3 and 3x+3y=7, choosing option a) to solve for x in the first equation can be advantageous because it allows for direct isolation of x. After solving for one variable, you can substitute its value into the other equation to find the second variable. It's important to review and simplify your equations whenever possible to minimize potential errors and check that your answers are reasonable, following mathematical principles and logic.