Question

A system of equations is shown below:
5x + 2y = 3 (equation 1)
2x – 3y = 1 (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

Answer choices:

Show that the solution to the system of equations 7x – y = 4 and 2x – 3y = 1 is the same as the solution to the given system of equations


Show that the solution to the system of equations 2x + 5y = 3 and 3x – 2y = 1 is the same as the solution to the given system of equations


Show that the solution to the system of equations 9x + 4y = 5 and 7x – y = 4 is the same as the solution to the given system of equations

Show that the solution to the system of equations –4x + 9y = 5 and 2x – 3y = 1 is the same as the solution to the given system of equations

Answer 2

@Orion1213 can you help me with this one too?

Answer 3

... i'm analyzing the problem... will get some coffee first...

Answer 4

(equation1) is replaced by [ (equation1) + 1*(equation2) ].
Choice 1 is correct.

Answer 5

how @math&ing001 ?

Answer 6

i agree with @math&ing001 ...

Answer 7

Choice 1 is the same as solving the given equations...

Answer 8

Simply sum up the two equations to get the first one.
(5x + 2y = 3)
+(2x – 3y = 1)

Answer 9

... combine like terms such as adding all x's and y's and constants...

Answer 10

you'll get 7x-y=4...

Answer 11

Thanks so much, you guys. I understand it now :) @Orion1213 @math&ing001

Answer 12

Welcome !