Question

The table below shows four systems of equations:

System 1

System 2

System 3

System 4

4x − 5y = 2
3x − y = 8


4x − 5y = 2
10x − 7y = 18


4x − 5y = 2
3x − 8y = 4


4x − 5y = 2
10x + 3y = 15


Which pair of systems will have the same solution?

System 1 and system 2, because the second equation in system 2 is obtained by adding the first equation in system 1 to two times the second equation in system 1.

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

Answer 1

Which pair of systems will have the same solution?

System 1 and system 2, because the second equation in system 2 is obtained by adding the first equation in system 1 to two times the second equation in system 1.

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.

System 1 and system 2, because the second equation in system 2 is obtained by adding the first equation in system 1 to three times the second equation in system 1.

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.

Answer 2

@hoblos

Answer 3

two systems have the same solution if the the equations of the second system are a combination of the equations of the first

so you have to check each of the cases given,
the first statement:
second equation in system 2 is obtained by adding the first equation in system 1 to two times the second equation in system 1

4x − 5y = 2
+ 2(3x − y = 8)
---------------
= 10x -7y = 18

so the first choice is true

Answer 4

thanks :D could you please help me with one more?

Answer 5

post the question and i'll try