Question

I've got a tough one for you guys.

The table below shows four systems of equations:
System 1 System 2 System 3 System 4
4x - 5y = 2 4x -5y = 2 4x - 5y = 2 4x - 5y = 2
3x - y = 8 3x - 8y = 4 13x - 8y = 26 10x + 3y = 15

Which pair of systems will have the same solution? (4 points)


A. System 1 and system 3, because the second equation in system 3 is obtained by adding the first equation in system 1 to two times the second equation in system 1.
B. System 2 and system 3, because the second equation in system 3 is obtained by adding the first equation in system 2 to two times the second equation in system 2.
C. System 2 and system 3, because the second equation in system 3 is obtained by adding the first equation in system 2 to three times the second equation in system 2.
D. System 1 and system 3, because the second equation in system 3 is obtained by adding the first equation in system 1 to three times the second equation in system 1.

Answer 1

@sourwing Can you help me after you're done there?

Answer 2

system 1. x = 38/11, y = 26/11

Answer 3

system 2. x = -4/17, y = -10/17

Answer 4

system 3. x = 38/11, y = 26/11

Answer 5

system 4. x = 81/62, y = 20/31

so systems 1 and 3 are the same.

Answer 6

Thanks Astro!

Answer 7

Np

Answer 8

@Astrophysics

Answer 9

It's D, because three times xD

Answer 10

That makes sense. Thank you twice!

Answer 11

You can try it out yourself just multiply first equation by 3 and add, and you'll get D :)