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

@ranga

Answer 3

Each answer choice has two equations: The second choice is the same for all and we can ignore it. The first choice is: "equation 1 is replaced with the sum of equation 1 and a multiple of equation 2"

From the first choice in each answer, subtract equation 1 and see if what is left is a multiple of equation 2. If yes then that is the answer.

I will do the first answer choice. Take the first equation 10x + y = 7
Subtract 6x – 2y = 3 (equation 1)
10x + y = 7
6x - 2y = 3
subtract
4x + 3y = 4
compare it to 5x + 3y = 4 (equation 2)
It is clearly not a multiple of equation 2 because 3y and 4 are the same but 6x and 4x are different. We can't find a multiple that can do that. So this is not the answer. Try the other three.

Answer 4

I meant 4x and 5x are different.

Answer 5

10x - y = 7
6x - 2y = 3

4x+y=4

Answer 6

I don't think it is

Answer 7

a multiple

Answer 8

11x-y=7
6x – 2y = 3

5x+y=4

Answer 9

11x+y=7
6x-2y=3

5x+3y=4

Answer 10

So it's D? @ranga

Answer 11

Yes. Well done.