Question

A system of equations and its solution are given below.

System A
x = 6y = 5
3x - 7y = -35
Solution: (-7, 2)

Choose the correct option that explains what steps were followed to obtain the system of equations below.

System B
x + 6y = 5
-25y = -50

A. To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 3. The solution to system B will not be the same as the solution to system A.

B. To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -5. The solution to system B will be the same as the solution to system A.

C. To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution to system B will be the same as the solution to system A.

D. To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 7. The solution to system B will not be the same as the solution to system A.

Answer 1

Answer: Option C. To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution to system B will be the same as the solution to system A.

First equation of system A multiplied by -3:
(-3)(x+6y=5)
(-3)(x)+(-3)(6)=(-3)(5)
-3x-18=-15

Sum of the second equation of system A and the first equation multiplied by -3:
(-3x-18)+(3x-7y)=(-15)+(-35)
-3x-18+3x-7y=-15-35
-25y=-50

System B
x+6y=5
-25y=-50 

Answer 2

Answer:

C. To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution to system B will be the same as the solution to system A.

Step-by-step explanation:

System A

x + 6y = 5

3x - 7y = -35

Solution: (-7, 2)

System B  

x + 6y = 5

-25y = -50

First equation is same in both system A  and B

To get system B, the second equation in system A was replaced by sum of that equation and first equation multiplied by -3

x + 6y = 5  (Multiply by -3)

-3x -18y =-15

now do the sum of 3x - 7y = -35  and -3x -18y =-15

3x - 7y = -35  

-3x -18y =-15

-----------------------

      -25 y = -50

The solution to system B will be the same as the solution to system A.