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

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

Step-by-step 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.

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.