To get system B, the 2x + 3y = 11 equation in system A was replaced by the sum of that equation and 3 times the -3x + 4y = -1 equation. The solution to system B is the same as the solution to system A.
How to solve for systems?
System A
In system A, there are two equations:
2x + 3y = 11
-3x + 4y = -1
To obtain this system of equations, started with the equation:
2x + 3y = 11
Then multiplied this equation by 3 and subtracted it from the second equation in the original system:
-3x + 4y = -1
This resulted in the second equation in system A:
-3x + 13y = -34
System B
In system B, two equations:
-x + 7y = -23
-3x + 13y = -34
To obtain this system of equations, replaced the second equation in system A with the sum of that equation and 3 times the first equation:
-3x + 13y = -34
Adding 3 times the first equation to the second equation:
3(2x + 3y = 11)
Which gives:
6x + 9y = 33
Subtracting this equation from the original second equation:
-3x + 13y = -34
This resulted in the second equation in system B:
-9y = -67
The solution to system B is:
x = 1
y = 7
This is the same as the solution to system A. This is because the two systems are equivalent, meaning they represent the same set of solutions.
Complete question:
Select the correct answer from each drop-down menu.
A system of equations and its solution are given below.
System A
2x + 3y = 11
-3x + 4y = -1
Complete the sentences to explain what steps were followed to obtain the system of equations below.
System B
-x + 7y = -23
-3x + 13y = -34
To get system B, the ____ equation in system A was replaced by the sum of that equation and ____ times the _____ equation. The solution to system B ____ the same as the solution to system A.