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 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 1

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

This is the correct answer because not only is it true but it also follows the property of solving systems of equations with adding the equations. To prove that it is true:

2nd equation in system #2 = 1st equation in system #1 + 2(2nd equation in system #1)

 10x − 7y = 18 == 4x − 5y = 2 + 2(3x − y = 8)
10x - 7y = 18 == 4x - 5y = 2 + 6x - 2y = 16
10x = 7y = 18 == 10x - 7y = 18

Answer 2

Answer:

its a hope this helps:)