Question

A system 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?

Answer 1

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

Answer 2

They don't want you to solve the equations right now, just show the next step. We're simply following the steps in this process by adding a multiple (1) of equation 2 and equation 1 together.