Question

A system of equations can be solved by elimination in the table below. 1 5x + 3y = 14 4x - 2y = -2 2 2(5x + 3y) = 2(14) 4x – 2y = -2 5x + 3y = 14 3(4x – 2y) = 3(-2) 3 10x + 6y = 28 4x - 2y = -2 5x + 3y = 14 12x – 6y = -6 4 10x + 6y = 28 12x 6y = -6 Does the system of equations on line 4 have the same solution set as the system of equations on line 1? Why or why not?

A.The system of equations in stel 4 is equivalent to the system of equation in step 1
The systems do not have the same solution set because the same ordered pair does not satisfy both systems.
B.The system of equations in step 4 is not equivalent to the system of equation in step 1.
The systems do not have the same solution because the same ordered pair does not satisfy both systems.
C.The system of equations in step 4 is
equivalentes to the system of equation in step 1
The systems have the same solution because the same ordered pair does satisfie both systems.
D.The system of equations in step 4 is not equivalentes to the system of equation in step 1
The systems have the same solution because the same ordered pair satisfies both systems. ​

Answer 1

Answer: C

The system is equivalent and has the same solutions.

Step-by-step explanation:

When multiplied by 2, the first equation is equal to the first one on line 4.

When multiplied by 3, the second equation on line 1 is equal to the second equation on line 4.

Since the equations are equal, the same ordered pair satisfies both equations.

I checked this on algebra nation and C is the correct answer.