Question

A system of equations and its solution are given below.

System A:
x - y = 3
-2x + 4y = -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 (first) equation in system A was replaced by the sum of that equation and the (second) equation multiplied by (2) The solution to system B is (the same) as the solution to system A.

Answer 1

The first equation in System A was replaced by the sum of that equation and the second equation multiplied by 2 to obtain System B. The solution to System B is the same as the solution to System A.

Step-by-step explanation:

To obtain System B from System A, the first equation in System A was replaced by the sum of that equation and the second equation multiplied by 2. Let's go step by step:

1. Multiply the second equation of System A by 2: 2(-2x + 4y) = 2(-2) -> -4x + 8y = -4
2. Add the first equation of System A to the result from step 1: (x - y) + (-4x + 8y) = 3 + (-4) -> -3x + 7y = -1

So, the resulting system is: x - y = 3 and -3x + 7y = -1. This is System B. The solution to System B is the same as the solution to System A.