Question

The table below shows four systems of equations:

System 1
4x − 5y = 2
3x − y = 4

System 2
4x − 5y = 2
10x − 21y = 10

System 3
4x − 5y = 2
24x − 47y = 22

System 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 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

Explanation:

We are given four systems of equations. We are asked to find which two sets have the same solution.

We find that in all the 4 systems, first equation 4x-5y =2 remains the same.

I option is wrong because

Equation I + 2times equation 2 in II system

gives 10x-7y =10 but given is 10x-21y =10 hence wrong.

Now compare 2 and 3

In system 2, I equation +2times second equation gives

24x-5y-42y =2+20 or

24x-47y =22

Hence system 2 and 3 are the same set of equations and give the same solution.