Question

To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this?

A. Because the system of equations actually has only one solution
B. Because the system of equations actually has no solution
C. Because the graphs of the two equations overlap each other
D. Because the graph of one of the equations does not exist

Answer 1

Answer:

Step-by-step explanation:

Ans c because in graph the line over lap each other and it means it have infinite many solution

Answer 2

◆GIVEN :

3x - 2y = 4 ---(1)

9x - 6y = 12 ----(2)

◆TO FIND :

Reason of why both these graphs shows one line.

◆SOLUTION :

According to linear combination ,

Multiplying equation (1) × 4

3x-2y = 4. ---(1) ×4

gives , 9x - 6y = 12 which is same as equation (2)

◆Solving both two equation gives 0=0 That is , not because equation have infinite solution , it's because both equation are same.

◆Graphing same equation leads in overlapping . That is the reason why henry saw one line.

◆And , equation (1) is parallel to equation (2) , as it is promotional.

So,

◆ANSWER - C. Because the graphs of the two equations overlap each other