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

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

any ideas?

Answer 3

no it really confuses me!!

Answer 4

ok. lets look at your problem.
it says equation 2 multiplied by 1.

which answer choice has equation 2 multiplied by 1?

Answer 5

isn't it the second choice?

Answer 6

no.
the second equation is 2x-3y=1
and if you multiply 1, you'll still get the same equation.

and the only choices that has this equation is A and D

Answer 7

no never mind... I mean the last one because the 2nd equation stayed the same cause its multiplied by 1

Answer 8

now you have to decide btw A and D

the problem says " to replace equation 1 with the sum of equation 1 and 2"

so you wanna add the 2 equations

Answer 9

and what do you get?