Final answer:
The simplified system of equations after multiplying the second equation by 2 is A. 14x + 6y = 120; -14x + 4y = 200, which facilitates the elimination of the variable x. Thus, the correct option is A.
Step-by-step explanation:
In the context of solving a system of linear equations through elimination, the method typically involves multiplying one or both equations by certain numbers to obtain an opposing coefficient for one of the variables.
This process simplifies the system by allowing us to add or subtract the equations to eliminate one variable and solve for the other. Given the options in the question, the simplified system after multiplying the second equation by 2 should have one equation with a positive coefficient and the other with a negative coefficient for the same variable, allowing them to cancel each other out.
The correct answer is A. 14x + 6y = 120; -14x + 4y = 200. This pair of equations allows the elimination of the variable x when the two are added together, as 14x and -14x cancel each other out, resulting in an equation with only the variable y.