Asystem of equations is shown below: . 6x – 2y = 3-> (equation 1). 5x + 3y = 4-> (equation 2). a student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. if equation 2 is multiplied by 1, which of the following steps should the student use for the proof?

From my research, the question had contained the following choices:

Show that the solution to the system of equations 10x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations
 
Show that the solution to the system of equations 10x – 2y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations
 
Show that the solution to the system of equations 11x – y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations
 
Show that the solution to the system of equations 11x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

Since all of the 2nd second equations of the choices are the same, we will ignore that. What we will do however, is to obtain the 1st equation of each choice and subtract it from the 1st given equation, and see if it is a multiple to the 2nd given equation. To show an example, let us take the equation in choice D:

11x + y = 7
6x – 2y = 3

5x + 3y = 4

As we can see, it is a multiple of the second given equation. Therefore, the correct answer is choice D.