Select the correct answer from each drop-down menu.

A system of equations and its solution are given below.

System A

x-y=3

-2x+4y = - 2

Solution: (5,2)

Complete the sentences to explain what steps were followed to obtain the system of equations below.

System B

x-y=3

2x=10

To get system B, the? equation in system A was replaced by the sum of that equation and the? equation multiplied by?. The solution to system B? the same as the solution to system A.

Fill in the blank where the question marks are.

second

first

4

is

second first 4 is

Step-by-step explanation:

In system B, the first equation is the same, so clearly the second equation has been replaced. The only other equation in the system is the first, so that is the one that is multiplied by some number.

The number it is multiplied by must make the y coefficient be the opposite of the y-coefficient in the second equation, so they cancel when added. That is, the multiplier times - 1 must be - 4, so the multiplier must be 4.

The purpose of doing this is to ensure the solution of System B is exactly the same as that of System A.